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group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) cusp singularity; automorphism group Singularities of surfaces or higher-dimensional varieties, Complex surface and hypersurface singularities, Automorphisms of surfaces and higher-dimensional varieties, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Global theory and resolution of singularities (algebro-geometric aspects) Finite automorphism groups of Cusp singularities

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) B. Weisfeiler, ''Abstract homomorphisms of big subgroups of algebraic groups,'' in: Topics in the Theory of Algebraic Groups, Notre Dame Math. Lectures (1982), pp. 135--181. Algebraic groups, Linear algebraic groups over arbitrary fields Abstract homomorphisms of big subgroups of algebraic groups

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(M\)-curve; \(M-1\)-curve; Gudkov conjecture; hyperboloid; isotopy of curves Topology of real algebraic varieties, Projective and enumerative algebraic geometry Congruences for \(M\)- and \((M-1)\)-curves with odd branches on a hyperboloid

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) characteristic \(p\); minimal surfaces of general type Automorphisms of surfaces and higher-dimensional varieties, Surfaces of general type, Finite ground fields in algebraic geometry On the automorphisms of surfaces of general type in positive characteristic. II

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space of irreducible plane curve singularities; minimal Tjurina number; Milnor number; Kodaira-Spencer map Laudal, O.A. , Martin, B. , and Pfister, G. , Moduli of irreducible plane curve singularities with the semi-group , Proc. Conf. Algebraic Geometry Berlin. Teubner-Texte 92 (1986). Families, moduli of curves (algebraic), Singularities of curves, local rings, Singularities in algebraic geometry Moduli of irreducible plane curve singularities with the semigroup \(<a,b>\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms; rational surfaces; quadratic transformations Rational and ruled surfaces, Automorphisms of surfaces and higher-dimensional varieties Rational surface automorphisms preserving cuspidal anticanonical curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(K3\) surfaces, automorphisms Automorphisms of surfaces and higher-dimensional varieties, Families, moduli, classification: algebraic theory, \(K3\) surfaces and Enriques surfaces Non-symplectic automorphisms of \(K3\) surfaces with one-dimensional moduli space

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) monomial automorphism; field extension with transcendence degree 2; rational fixed field; purely transcendental extension Hajja, M., A note on monomial automorphisms, J. Algebra, 85, 243-250, (1983) Transcendental field extensions, Separable extensions, Galois theory, Rational points A note on monomial automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; Hilbert scheme of points; hypersurface Automorphisms of surfaces and higher-dimensional varieties, Parametrization (Chow and Hilbert schemes), Hypersurfaces and algebraic geometry On automorphisms of Hilbert squares of smooth hypersurfaces

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Sato-Tate group; abelian threefold; twists Arithmetic ground fields for curves, Abelian varieties of dimension \(> 1\), Galois representations The twisting Sato-Tate group of the curve \(y^2 = x^{8} - 14x^4 + 1\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Goppa linear error-correcting codes; curves over finite fields; curves with the maximal number of rational points; Klein quartic Hansen, J. P.: Group codes on algebraic curves. Mathematica Gottingensis, Heft 9, Feb. 1987 Arithmetic ground fields for curves, Finite ground fields in algebraic geometry, Linear codes (general theory), Software, source code, etc. for problems pertaining to algebraic geometry, Decoding Group codes on algebraic curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Matthews, G. L., The Weierstrass semigroup of an \textit{m}-tuple of collinear points on a Hermitian curve, (Finite Fields and Applications, Lect. Notes Comput. Sci., vol. 2948, (2004), Springer Berlin), 12-24 Riemann surfaces; Weierstrass points; gap sequences, Arithmetic theory of algebraic function fields, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry, Arithmetic ground fields for curves The Weierstrass semigroup of an \(m\)-tuple of collinear points on a Hermitian curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli space; symplectic bundle; automorphism; Higgs bundle; complex projective curve Biswas, I., Gómez, T. L., and Muñoz, V., \textit{Automorphisms of moduli spaces of symplectic}\textit{bundles}, Internat. J. Math. 23 (2012), no. 5, 1250052, 27pp. Vector bundles on curves and their moduli, Torelli problem, Automorphisms of curves Automorphisms of moduli spaces of symplectic bundles

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) groups of automorphisms; inner automorphisms; Fredholm operators; indices of operators; \(K_1(\mathbb S_1)\); semi-direct products of groups; minimal primes; algebras of one-sided inverses of polynomial algebras Automorphisms and endomorphisms, Ordinary and skew polynomial rings and semigroup rings, Jacobian problem, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Birational automorphisms, Cremona group and generalizations, Automorphisms of curves, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) \(K_1(\mathbb S_1)\) and the group of automorphisms of the algebra \(\mathbb S_2\) of one-sided inverses of a polynomial algebra in two variables.

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Nagata automorphism; nonlinear orthogonal group; invariant quadratic form Lamy S. Automorphismes polynomiaux préservant une action de groupe. Bol Soc Mat Mexicana (3), 2003, 9(1): 1--19 Group actions on varieties or schemes (quotients), Automorphisms of surfaces and higher-dimensional varieties, Actions of groups on commutative rings; invariant theory, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Group actions on affine varieties Polynomial automorphism, preserving a group action

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) birational automorphisms; biregular automorphisms; quasiprojective variety; Jordan group; strongly Jordan group Birational automorphisms, Cremona group and generalizations, Elliptic curves, Infinite automorphism groups Jordan properties of automorphism groups of certain open algebraic varieties

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Discriminant; Hyperelliptic curves over finite fields; Public-key cryptography Encinas, L. Hernández; Menezes, A. J.; Masqué, J. Muñoz: Isomorphism classes of genus-2 hyperelliptic curves over finite fields. Appl. algebra eng., commun. Comput. 13, No. 1, 57-65 (2002) Finite ground fields in algebraic geometry, Curves over finite and local fields, Applications to coding theory and cryptography of arithmetic geometry, Cryptography Isomorphism classes of genus-2 hyperelliptic curves over finite fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Klein surfaces; genus; Riemann surfaces; NEC groups; alternating groups; Hurwitz groups; \(H^*\)-groups Generators, relations, and presentations of groups, Fuchsian groups and their generalizations (group-theoretic aspects), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Compact Riemann surfaces and uniformization, Automorphisms of curves, Riemann surfaces; Weierstrass points; gap sequences, Classification theory of Riemann surfaces, Discrete subgroups of Lie groups Alternating groups as automorphism groups of Riemann surfaces.

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Zariski problem; fundamental group DOI: 10.2206/kyushumfs.39.133 Coverings in algebraic geometry On the fundamental group of the complement to a maximal cuspidal plane curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) curves with automorphisms; Galois covers; Hurwitz spaces; infinite Grassmannians Automorphisms of curves, Coverings of curves, fundamental group, Families, moduli of curves (algebraic), Grassmannians, Schubert varieties, flag manifolds Curves with a group action and Galois covers via infinite Grassmannians

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane curve; complement of a nodal curve in \(\mathbb{P}^ 2\); Zariski problem; abelianness of the fundamental group Homotopy theory and fundamental groups in algebraic geometry, Curves in algebraic geometry, Coverings in algebraic geometry Fundamental group of the complement of affine plane curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) modular curves; Jacobians; component groups; degeneracy maps Arithmetic aspects of modular and Shimura varieties, Jacobians, Prym varieties On component groups of \(J_0(N)\) and degeneracy maps

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; fundamental group; Fuchsian group; normal surface singularity; logarithmic Kodaira dimension Singularities of surfaces or higher-dimensional varieties, Group actions on varieties or schemes (quotients), Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Automorphismes des surfaces non complètes, groupes Fuchsiens et singularités quasihomogènes

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) exponential sums; Weil's Riemann hypothesis; zeta functions; curves; function fields in one variable Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) Curves, function fields and the Riemann hypothesis

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) quartic Hessian surfaces; group of birational automorphisms; K3 surface; Leech lattice; Leech roots Dolgachev, [Dolgachev and Keum 02] I.; Keum, J., Birational automorphisms of quartic Hessian surfaces., \textit{Trans. Amer. Math. Soc.}, 354, 3031-3057, (2002) Birational automorphisms, Cremona group and generalizations, \(K3\) surfaces and Enriques surfaces, Automorphism groups of lattices, Automorphisms of surfaces and higher-dimensional varieties Birational automorphisms of quartic Hessian surfaces

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic curves; automorphism groups; Galois covers Automorphisms of curves, Coverings of curves, fundamental group Riemann surfaces with a large abelian group of automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) F. Sairaiji, Formal groups of certain \(\q\)-curves over quadratic fields , Osaka J. Math. 39 (2002), 223-243. Elliptic curves over global fields, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Formal groups, \(p\)-divisible groups Formal groups of certain \(\mathbb Q\)-curves over quadratic fields.

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic curve; Selmer group; Mordell-Weil group Elliptic curves over global fields, Elliptic curves On the Selmer groups and Mordell-Weil groups of elliptic curves \(y^2 = x(x \pm p)(x \pm q)\) over imaginary quadratic number fields of class number one

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism groups; derived categories; canonical algebras; coherent sheaves; finite dimensional algebras; selfequivalences; exact functors; weighted projective lines; tubular mutations; braid groups; translations Lenzing, H.; Meltzer, H., The automorphism group of the derived category for a weighted projective line, Comm. Algebra, 28, 1685, (2000) Representations of orders, lattices, algebras over commutative rings, Vector bundles on curves and their moduli, Braid groups; Artin groups, Automorphisms and endomorphisms, Module categories in associative algebras The automorphism group of the derived category for a weighted projective line

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) moduli spaces of curves; Picard groups; symmetric mapping class groups Families, moduli of curves (algebraic), Divisors, linear systems, invertible sheaves Picard groups of moduli spaces of curves with symmetry

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fundamental group of the complement of a curve; torus knot Coverings of curves, fundamental group, Homotopy theory and fundamental groups in algebraic geometry, Special algebraic curves and curves of low genus, Fundamental group, presentations, free differential calculus On the fundamental groups of complements of toral curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic K-theory; Brauer group; Galois cohomology group; Chow groups S. Bloch, Torsion algebraic cycles, \(K_2\), and Brauer groups of function fields , The Brauer group (Sem., Les Plans-sur-Bex, 1980), Lecture Notes in Math., vol. 844, Springer, Berlin, 1981, pp. 75-102. \(K\)-theory of global fields, \(K_2\) and the Brauer group, Galois cohomology, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Brauer groups of schemes, Grothendieck groups, \(K\)-theory and commutative rings Torsion algebraic cycles, \(K_ 2,\) and Brauer groups of function fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Jacobian with nontrivial endomorphism ring; moduli space of smooth projective irreducible complex curves C. Ciliberto and G. Van Der Geer , Subvarieties of the moduli space of curves parametrizing Jacobians with non-trivial endomorphisms , Am. J. Math. 114 (1991), 551-570. Families, moduli of curves (algebraic), Jacobians, Prym varieties Subvarieties of the moduli space of curves parametrizing Jacobians with non-trivial endomorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Inoue surfaces; Kodaira surfaces; automorphisms; Jordan property Birational automorphisms, Cremona group and generalizations, Compact complex surfaces, Automorphisms of surfaces and higher-dimensional varieties Automorphism groups of Inoue and Kodaira surfaces

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) order of the automorphism group of surfaces of general type; invariant locus; Weierstrass points; discriminantal divisor Corti, Polynomial bounds for the number of automorphisms of a surface of general type, Ann. Sci. École Norm. Sup. (4) 24 (1) pp 113-- (1991) Surfaces of general type, Automorphisms of surfaces and higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations Polynomial bounds for the number of automorphisms of a surface of general type

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) number of automorphisms of a surface of general type; minimal fibration DOI: 10.2748/tmj/1178225677 Automorphisms of surfaces and higher-dimensional varieties, Birational automorphisms, Cremona group and generalizations, Families, fibrations in algebraic geometry Bounds of automorphism groups of genus 2 fibrations

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; positive characteristic; Artin-Schreier curves Automorphisms of curves, Algebraic functions and function fields in algebraic geometry, Finite ground fields in algebraic geometry An elementary abelian \(p\)-cover of the Hermitian curve with many automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann surfaces, Teichmüller theory for Riemann surfaces, Riemann surfaces; Weierstrass points; gap sequences, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Hyperelliptische Riemannsche Flächen: Automorphismengruppen, Überlagerungen und Teichmüllerräume. (Hyperelliptic Riemann surfaces: automorphism groups, coverings and Teichmüller spaces)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) outer Galois representation; Grothendieck conjecture \begingroup Y. Hoshi: Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero , Nagoya Math. J. 203 (2011), 47-100. \endgroup Coverings of curves, fundamental group, Families, moduli of curves (algebraic) Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Galois cohomology; generalized flag variety; Picard group; Brauer group; Chow group Peyré, G, A review of adaptive image representations, IEEE J. Sel. Top. Signal Process., 5, 896-911, (2011) Grassmannians, Schubert varieties, flag manifolds, Galois cohomology, Parametrization (Chow and Hilbert schemes), Brauer groups of schemes Function fields of homogeneous varieties and Galois cohomology

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) homographies; quadratic fields; group \(\mathrm{SL}_2(\mathrm{Z}[i])\) Structure of modular groups and generalizations; arithmetic groups, Quadratic extensions, Rational and birational maps, Linear algebraic groups over global fields and their integers On groups of linear substitutions with coefficients belonging to imaginary quadratic fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hermitian form; \(u\)-invariant; \(p\)-adic curve Bilinear and Hermitian forms, Quadratic forms over general fields, Algebraic theory of quadratic forms; Witt groups and rings, Algebraic functions and function fields in algebraic geometry, Finite-dimensional division rings, Rings with involution; Lie, Jordan and other nonassociative structures Hermitian \(u\)-invariants over function fields of \(p\)-adic curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) inverse mapping; polynomial mapping; Jacobian conjecture; Gröbner bases; algebraic group actions; derivation A. van den Essen, \textit{Seven lectures on polynomial automorphisms}, in: \textit{Automor-phisms of Affine Spaces} (Curaçao, 1994), Kluwer Acad. Publ., Dordrecht, 1995, pp. 3-39. Polynomial rings and ideals; rings of integer-valued polynomials, Automorphisms of curves, Polynomials in general fields (irreducibility, etc.) Seven lectures on polynomial automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) compactification of orbit space; arithmetic group; genus of algebraic curve over finite field Wolfgang Radtke, Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall, J. Reine Angew. Math. 363 (1985), 191 -- 200 (German). Arithmetic ground fields for curves, Arithmetic theory of algebraic function fields, Structure of modular groups and generalizations; arithmetic groups, Finite ground fields in algebraic geometry, Algebraic functions and function fields in algebraic geometry, Kleinian groups (aspects of compact Riemann surfaces and uniformization), Group actions on varieties or schemes (quotients), Fuchsian groups and their generalizations (group-theoretic aspects) Diskontinuierliche arithmetische Gruppen im Funktionenkörperfall. (Discontinuous arithmetic groups in case of function field)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) purely transcendental extension; degree of transcendency; unirational fields Ohm, J.: On subfields of rational function fields. Arch. math. 42, 136-138 (1984) Transcendental field extensions, Arithmetic theory of algebraic function fields, Rational points On subfields of rational function fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) graded simple Lie algebras; connected reductive groups; equivariant polynomial automorphisms; irreducible representations A. Kurth:Equivariant Polynomial Automorphisms. Ph.D. Thesis Basel (1996). Representation theory for linear algebraic groups, Rational and birational maps, Group actions on varieties or schemes (quotients), Graded Lie (super)algebras Equivariant polynomial automorphisms of \(\Theta\)-representations

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Curve; isomorphism class; fundamental group Tamagawa, A., \textit{finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups}, J. Algebraic Geom., 13, 675-724, (2004) Arithmetic ground fields for curves, Finite ground fields in algebraic geometry, Jacobians, Prym varieties, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Coverings of curves, fundamental group Finiteness of isomorphism classes of curves in positive characteristic with prescribed fundamental groups

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group of analytic algebra; formal algebra; Levi subgroup Müller, G.: Reduktive automorphismengruppen analytischer C-algebren. J. reine angew. Math. 364, 26-34 (1986) Analytic algebras and generalizations, preparation theorems, Complex Lie groups, group actions on complex spaces, Infinite automorphism groups, Group actions on varieties or schemes (quotients) Reduktive Automorphismengruppen analytischer \({\mathbb{C}}\)-Algebren

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) surface bundles over surfaces; branched covering; minimal base genus problem; upper bound General topology of 4-manifolds, Riemann surfaces, Low-dimensional topology of special (e.g., branched) coverings, Riemann surfaces; Weierstrass points; gap sequences, Coverings of curves, fundamental group From automorphisms of Riemann surfaces to smooth \(4\)-manifolds

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms; hypersurface DOI: 10.1007/s11856-012-0177-y Automorphisms of surfaces and higher-dimensional varieties, Hypersurfaces and algebraic geometry On the order of an automorphism of a smooth hypersurface

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) join-type curves; fundamental groups C. Eyral and M. Oka, On the fundamental groups of non-generic R-join-type curves, Experimental and Theoretical Methods in Algebra, Geometry and Topology, Springer Proceedings in Mathematics & Statistics. (to appear). Coverings of curves, fundamental group, Coverings in algebraic geometry, Homotopy theory and fundamental groups in algebraic geometry, Singularities of curves, local rings, Local rings and semilocal rings, Singularities in algebraic geometry, Special algebraic curves and curves of low genus, Plane and space curves Fundamental groups of join-type curves -- achievements and perspectives

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) abelian groups of automorphisms of compact Riemann surfaces; large groups of automorphisms Automorphisms of curves, Coverings of curves, fundamental group Riemann surfaces with a quasi large abelian group of automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) list decoding; algebraic-geometric codes; cyclotomic function fields; Galois extensions; Reed-Solomon codes; Frobenius automorphisms V. Guruswami: Cyclotomic function fields, Artin-Frobenius automorphisms, and list error-correction with optimal rate, Algebra and Number Theory 4 (2010), 433--463. Geometric methods (including applications of algebraic geometry) applied to coding theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Applications to coding theory and cryptography of arithmetic geometry, Decoding, Computational aspects of algebraic curves, Curves of arbitrary genus or genus \(\ne 1\) over global fields Cyclotomic function fields, Artin-Frobenius automorphisms, and list error correction with optimal rate

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) elliptic surfaces; action of automorphisms on cohomology Cai, J.-X., Automorphisms of elliptic surfaces, inducing the identity in cohomology, J. Algebra, 322, 12, 4228-4246, (2009) Elliptic surfaces, elliptic or Calabi-Yau fibrations Automorphisms of elliptic surfaces, inducing the identity in cohomology

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Coverings of curves, fundamental group, Arithmetic ground fields for curves, Dessins d'enfants theory On fields of definition of an algebraic curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) fundamental group; generic projection; curves and singularities; branch curve DOI: 10.1007/s10114-009-6473-8 Homotopy theory and fundamental groups in algebraic geometry, Coverings of curves, fundamental group, Surfaces and higher-dimensional varieties, Computational aspects of algebraic curves, Computational aspects of algebraic surfaces The fundamental group of the complement of the branch curve of \(\mathbb {CP}^{1} \times T\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Grassmann graph; residue class ring; Grassmann space; automorphism; maximum clique Graphs and abstract algebra (groups, rings, fields, etc.), Homogeneous spaces and generalizations Automorphisms of Grassmann graphs over a residue class ring

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) V.M. Bukhshtaber, D.V. Leĭ kin and V.Z. Ènol'skiĭ: \(\sigma\)-functions of \((n, s)\)-curves , Russian Math. Surveys 54 (1999), 628-629. Analytic theory of abelian varieties; abelian integrals and differentials, Relationships between algebraic curves and integrable systems, Period matrices, variation of Hodge structure; degenerations \(\sigma\)-functions of \((n,s)\)-curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) finite field; maximal curve; Hermitian curve; Galois covering Arithmetic ground fields for curves, Automorphisms of curves, Finite ground fields in algebraic geometry, Curves over finite and local fields, Coverings of curves, fundamental group \(\mathbb{F}_{p^2}\)-maximal curves with many automorphisms are Galois-covered by the Hermitian curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Hilbert scheme; automorphisms; fixed points Boissière, S., Automorphismes naturels de l'espace de Douady de points sur une surface, Canad. J. Math., 64, no. 1, 3-23, (2012) Parametrization (Chow and Hilbert schemes), Automorphisms of surfaces and higher-dimensional varieties, Compact complex surfaces, Complex Lie groups, group actions on complex spaces, Bergman spaces and Fock spaces Natural automorphisms of the Douady space of points on a surface

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) deformation functor; 2-holomorphic differentials; automorphisms; local-global principle Kontogeorgis, Polydifferentials and the deformation functor of curves with automorphisms, J. Pure Appl. Algebra 210 (2) pp 551-- (2007) Automorphisms of curves, Families, moduli of curves (algebraic) Polydifferentials and the deformation functor of curves with automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) transcendental invariant subfield; rational function field; automorphisms Chu, H, Orthogonal group actions on rational function fields, Bull. Inst. Math. Acad. Sinica, 16, 115-122, (1988) Geometric invariant theory, Arithmetic theory of algebraic function fields, Transcendental field extensions, Group actions on varieties or schemes (quotients) Orthogonal group actions on rational function fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Zariski problem; fundamental group of the complement of an algebraic curve Homotopy theory and fundamental groups in algebraic geometry, Curves in algebraic geometry, Classical real and complex (co)homology in algebraic geometry On the structure of the fundamental group of the complement of algebraic curves in \(\mathbb{C}^ 2\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Blanc, J; Dubouloz, A, Affine surfaces with a huge group of automorphisms, Int. Math. Res. Not. IMRN, 2, 422-459, (2015) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms of surfaces and higher-dimensional varieties Affine surfaces with a huge group of automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) surface of general type; automorphism; cohomology Automorphisms of surfaces and higher-dimensional varieties, Surfaces of general type Automorphisms of an irregular surface with low slope acting trivially in cohomology

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Curves over finite and local fields, Number-theoretic algorithms; complexity, Computational aspects of algebraic curves Computing in Picard groups of projective curves over finite fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) linear algebraic group; outer automorphism; Hermitian form; involution Linear algebraic groups over arbitrary fields, Automorphisms of infinite groups, Automorphism groups of groups, Group schemes Outer automorphisms of classical algebraic groups

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) neutral equation; oscillation; deviating argument; comparison theorems DOI: 10.1016/S0022-4049(00)00062-1 Characteristic classes and numbers in differential topology, Families, moduli of curves (analytic), Cohomology of groups, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Homology of classifying spaces and characteristic classes in algebraic topology, Finite transformation groups Periodic surface automorphisms and algebraic independence of Morita-Mumford classes

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) positive entropy; quotient of a torus; quotient singularity; minimal model program [38] Zhang (D-Q).-- Algebraic varieties with automorphism groups of maximal rank, Math. Ann., 355(1), p.~131-146 (2013). &MR~30 | &Zbl~1262. Complex Lie groups, group actions on complex spaces, Automorphisms of surfaces and higher-dimensional varieties, Minimal model program (Mori theory, extremal rays), Topological entropy Algebraic varieties with automorphism groups of maximal rank

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(K3\) surfaces; automorphisms; log rational surfaces \(K3\) surfaces and Enriques surfaces, Automorphisms of surfaces and higher-dimensional varieties, Singularities of surfaces or higher-dimensional varieties, Rational and ruled surfaces, Fano varieties, Research exposition (monographs, survey articles) pertaining to algebraic geometry Automorphisms of \(K3\) surfaces and their applications

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) semisimple polynomial automorphisms; Zariski closed sets; diagonalizable automorphisms; infinite dimensional algebraic varieties S. Kaliman, M. Koras, L. Makar-Limanov, P. Russell, \(\mathbb{C}\)\^{}\{*\}-\textit{actions on} \(\mathbb{C}\)\^{}\{3\}\textit{are linearizable}, Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 63-71 (electronic). Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Birational automorphisms, Cremona group and generalizations A characterization of semisimple plane polynomial automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Families, moduli of curves (algebraic), (Equivariant) Chow groups and rings; motives, Elliptic curves Rational Picard group of moduli of pointed hyperelliptic curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) divisibility; divisor class group of curves; finite field; computation of the discrete logarithm G. Frey; H. Rück, A remark concerning \(m\)-divisibility and the discrete logarithm in the divisor class group of curves, Mathematics of Computation, 62, 865, (1994) Computational aspects of algebraic curves, Arithmetic ground fields for curves, Number-theoretic algorithms; complexity, Curves over finite and local fields, Finite ground fields in algebraic geometry, Picard groups A remark concerning \(m\)-divisibility and the discrete logarithm in the divisor class group of curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms of polynomial algebras; affine automorphisms; tame automorphisms; closed automorphism groups Éric Edo, ``Closed subgroups of the polynomial automorphism group containing the affine subgroup'', to appear in \(Transform. Groups\) Polynomials over commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials, Birational automorphisms, Cremona group and generalizations Closed subgroups of the polynomial automorphism group containing the affine subgroup

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) polynomial automorphisms; tame automorphisms; stably tame automorphisms Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Morphisms of commutative rings, Polynomials over commutative rings, Birational automorphisms, Cremona group and generalizations Length four polynomial automorphisms

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; character theory; Riemann-Hurwitz relation Compact Riemann surfaces and uniformization, Riemann surfaces; Weierstrass points; gap sequences, Ordinary representations and characters The character theory of groups and automorphism groups of Riemann surfaces. II

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) polynomial automorphism; Jung-van der Kulk theorem; multidegree of automorphism Edo, Some families of polynomial automorphisms II, Acta Math. Vietnam. 32 pp 155-- (2007) Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) Some families of polynomial automorphisms. II.

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) postulation; rational curve; Hilbert function; fat point; \(m\)-point Ballico, E.: Postulation of a general union of an m-point and a general smooth rational curve. Mediter. J. Math. \textbf{12}, 281-300 (2015). 10.1007/s00009-014-0418-x Projective techniques in algebraic geometry, Divisors, linear systems, invertible sheaves, Riemann surfaces; Weierstrass points; gap sequences Postulation of a general union of an \(m\)-point and a general smooth rational curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) plane quartic curves; function field; Galois group K. Miura - H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra, 226 (2000), pp. 283-294. Zbl0983.11067 MR1749889 Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry Field theory for function fields of plane quartic curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) principal bundle; torus bundle; Levi reduction; adjoint bundle; Hermitian-Einstein connection Group actions on varieties or schemes (quotients), Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Other connections, Automorphisms of surfaces and higher-dimensional varieties Automorphism group of principal bundles, Levi reduction and invariant connections

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) arrangements; combinatorial invariance; Milnor fiber; Catalan equation; monodromies; Alexander polynomials; Mordell-Weil groups A. Libgober, On combinatorial invariance of the cohomology of the Milnor fiber of arrangements and the Catalan equation over function fields. Arrangements of hyperplanes-Sapporo 2009, 175-187, Adv. Stud. Pure Math., 62, Math. Soc. Japan, Tokyo, 2012. Coverings of curves, fundamental group, Relations with arrangements of hyperplanes, Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry), Relations with algebraic geometry and topology On combinatorial invariance of the cohomology of the Milnor fiber of arrangements and the Catalan equation over function fields

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) group of polynomial automorphisms of a real compact affine variety M. W. Hirsch, Automorphisms of compact affine varieties, in Global Analysis in Modern Mathematics (Orono, ME, 1991; Walthom, MA, 1992), Publish or Perish, Houston, TX, 1993, pp. 227--245. Topological properties of groups of homeomorphisms or diffeomorphisms, Real-analytic and semi-analytic sets, Groups acting on specific manifolds Automorphisms of compact affine varieties

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphisms; curves; hyperelliptic Riemann surface Bjorn Poonen, Varieties without extra automorphisms. I. Curves, Math. Res. Lett. 7 (2000), no. 1, 67 -- 76. , https://doi.org/10.4310/MRL.2000.v7.n1.a6 Bjorn Poonen, Varieties without extra automorphisms. II. Hyperelliptic curves, Math. Res. Lett. 7 (2000), no. 1, 77 -- 82. Automorphisms of curves, Arithmetic algebraic geometry (Diophantine geometry), Riemann surfaces; Weierstrass points; gap sequences, Elliptic curves Varieties without extra automorphisms. II: Hyperelliptic curves

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Morita-Mumford classes; mapping class groups; hyperelliptic curves; gap sequences; Bernoulli numbers DOI: 10.1016/S0166-8641(01)00272-3 General low-dimensional topology, Special algebraic curves and curves of low genus, Families, moduli of curves (analytic), Riemann surfaces; Weierstrass points; gap sequences Weierstrass points and Morita-Mumford classes on hyperelliptic mapping class groups

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic automorphism; complete intersection; affine variety Affine geometry, Hypersurfaces and algebraic geometry Automorphisms of affine smooth varieties

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) actions of reductive groups; affine space; linearization; flexibility; density property; infinite dimensional automorphism groups; holomorphic factorization Complex Lie groups, group actions on complex spaces, Group actions on affine varieties, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Group actions on varieties or schemes (quotients), Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Oka principle and Oka manifolds Manifolds with infinite dimensional group of holomorphic automorphisms and the linearization problem

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) affine plane; triangular automorphism; polynomial automorphism Jean-Philippe Furter, ``On the length of polynomial automorphisms of the affine plane'', Math. Ann.322 (2002) no. 2, p. 401-411 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Actions of groups on commutative rings; invariant theory On the length of polynomial automorphisms of the affine plane

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) automorphism group; Galois point; icosahedral group; plane curve Automorphisms of curves, Plane and space curves Smooth plane curves with outer Galois points whose reduced automorphism group is \(A_5\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Riemann surfaces; Fuchsian groups; automorphisms; epimorphisms; smooth quotients; cyclic groups; dihedral groups; metacyclic groups; genus; genera Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Fuchsian groups and their generalizations (group-theoretic aspects), Automorphisms of curves On the genera of compact Riemann surfaces admitting \(C_p\times D_m\) as a group of automorphisms.

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) order of automorphism group; K3 surface S. Kondo, The maximum order of finite groups of automorphisms of \(K3\) surfaces, Amer. J. Mathematics 121 (1999), 1245-1252. Automorphisms of surfaces and higher-dimensional varieties, \(K3\) surfaces and Enriques surfaces The maximum order of finite groups of automorphisms of \(K3\) surfaces

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Tate module; abelian variety; function field; Galois group; transcendence degree Separable extensions, Galois theory, Abelian varieties and schemes On Galois groups of function fields of finite type over \(\mathbb{Q}\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) S. Kuroda, Automorphisms of a polynomial ring which admit reductions of type I, Publ. RIMS Kyoto Univ. 45 (2009), 907-917. Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Derivations and commutative rings Automorphisms of a polynomial ring which admit reductions of type I

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Algebraic functions and function fields in algebraic geometry, Coverings of curves, fundamental group, Automorphisms of curves Correction to ``The automorphism group of a cyclic \(p\)-gonal curve''

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) Mordell-Lang; Manin-Mumford; quantifier elimination; stability theory; differentially closed fields; separably closed fields Model-theoretic algebra, Classification theory, stability, and related concepts in model theory, Abelian varieties of dimension \(> 1\), Rational points, Algebraic functions and function fields in algebraic geometry On function field Mordell-Lang and Manin-Mumford

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) \(K\)-groups; Brauer groups; duality Galois cohomology, Brauer groups of schemes, Symbols and arithmetic (\(K\)-theoretic aspects), Higher symbols, Milnor \(K\)-theory, \(K_2\) and the Brauer group On the Brauer group of Laurent series and rational function fields and its duality with K-groups

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) equivalent polynomials; automorphisms Penelope G. Wightwick, Equivalence of polynomials under automorphisms of \Bbb C&sup2;, J. Pure Appl. Algebra 157 (2001), no. 2-3, 341 -- 367. Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Polynomials in real and complex fields: location of zeros (algebraic theorems) Equivalence of polynomials under automorphisms of \(\mathbb{C}^2\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) rational points; Jacobian of the Fermat curve Tzermias P.: Mordell-Weil groups of the Jacobian of the 5-th Fermat curve. Proc. Amer. Math. Soc. 125, 663--668 (1997) Jacobians, Prym varieties, Rational points, Arithmetic ground fields for curves, Higher degree equations; Fermat's equation Mordell-Weil groups of the Jacobian of the 5-th Fermat curve

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) algebraic stacks; étale cohomology; Brauer group; gerbe Poma, Flavia, Étale cohomology of a DM curve-stack with coefficients in \(\mathbb{G}_m\), Monatsh. Math., 169, 1, 33-50, (2013) Étale and other Grothendieck topologies and (co)homologies, Generalizations (algebraic spaces, stacks) Étale cohomology of a DM curve-stack with coefficients in \(\mathbb G _m\)

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) coordinate ring of an irreducible affine curve; Pic; Picard group DOI: 10.1007/BF01215648 Picard groups, Singularities of curves, local rings Picard groups of singular affine curves over a perfect field

group of automorphisms; function fields; affine curves Kontogeorgis, A.I.: The group of automorphisms of the function fields of the curve \(x^n + y^ m + 1 = 0\). J. Number Theory \textbf{72}, 110-136 (1998) Arithmetic theory of algebraic function fields, Algebraic functions and function fields in algebraic geometry, Curves of arbitrary genus or genus \(\ne 1\) over global fields The group of automorphisms of the function fields of the curve \(x^n+y^m+1=0\) abelian variety; finite field; endomorphism ring; rational points Arithmetic ground fields for abelian varieties, Finite ground fields in algebraic geometry, Abelian varieties of dimension \(> 1\), Rational points The structure of the group of rational points of an abelian variety over a finite field