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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 \(x^n+y^m+1=0\) Teichmüller space; morphism; coarse moduli spaces Families, moduli of curves (analytic), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (algebraic), Teichmüller theory for Riemann surfaces, Fine and coarse moduli spaces Morphisms between the moduli spaces of curves with generalized Teichmüller structure

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 \(x^n+y^m+1=0\) differential function field; algebraic differential equations; ADE; Galois theory; no movable singularity; Picard-Vessiot extension; Kolchin's theory; normal function fields; linearization property; complete integrable Hamiltonian systems; Euler equations Buium, A.: ''Differential function fields and moduli of algebraic varieties'', Lecture notes in math. 1226 (1986) Differential algebra, Algebraic functions and function fields in algebraic geometry, Algebraic moduli problems, moduli of vector bundles, Abstract differential equations, Hamilton's equations, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Research exposition (monographs, survey articles) pertaining to field theory Differential function fields and moduli of 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 \(x^n+y^m+1=0\) anabelian geometry Mohamed Saïdi, On complete families of curves with a given fundamental group in positive characteristic, Manuscripta Math. 118 (2005), no. 4, 425 -- 441. Coverings of curves, fundamental group, Étale and other Grothendieck topologies and (co)homologies, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory) On complete families of curves with a given fundamental group in positive characteristic

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 \(x^n+y^m+1=0\) multiplicative group; algebraic curves; height functions; finiteness result; rational points P. Habegger, A Bogomolov property for curves modulo algebraic subgroups , Bull. Soc. Math. France 137 (2009), 93--125. Heights, Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems, Arithmetic ground fields for curves, Counting solutions of Diophantine equations, Rational points, Global ground fields in algebraic geometry A Bogomolov property for curves modulo algebraic subgroups

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 \(x^n+y^m+1=0\) natural deformations of an abelian cover; automorphism group; coarse moduli spaces of abelian covers; moduli space of varieties with ample canonical class; irreducible components of the moduli Fantechi B, Pardini R. Automorphism and moduli spaces of varieties with ample canonical class via deformations of abelian covers. Comm Algebra, 1997, 25: 1413--1441 Automorphisms of curves, Coverings in algebraic geometry, Algebraic moduli problems, moduli of vector bundles Automorphisms and moduli spaces of varieties with ample canonical class via deformations of abelian covers

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 \(x^n+y^m+1=0\) Weierstrass \(n\)-semigroup; smooth curve; semigroup of non-gaps; non-special line bundle Riemann surfaces; Weierstrass points; gap sequences, Projective techniques in algebraic geometry On the non-special part of the Weierstrass semigroup of \(n\)-points of a smooth curve (its minimal number of generators)

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 \(x^n+y^m+1=0\) 5-dimensional subvariety; Grassmann variety; automorphisms \(n\)-folds (\(n>4\)), Automorphisms of surfaces and higher-dimensional varieties, Grassmannians, Schubert varieties, flag manifolds On a 5-dimensional non-singular rational subvariety of Grassmann variety Gr(5,1). III: Automorphisms of this variety

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 \(x^n+y^m+1=0\) \(R\)-equivalence; semisimple algebraic group; arithmetical field; flasque resolution; rationality of variety Chernousov, V. I.; Timoshenko, L. M.: On the group of R-equivalence classes of semisimple groups over arithmetic fields. Algebra i analiz 11, No. 6, 191-221 (1999) Group varieties, Rational and unirational varieties, Classical groups, Linear algebraic groups over global fields and their integers, Global ground fields in algebraic geometry, Local ground fields in algebraic geometry On the group of \(R\)-equivalence classes of semisimple groups over arithmetic 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 \(x^n+y^m+1=0\) Kharlamov, V, Topology, moduli and automorphisms of real algebraic surfaces, Milan J. Math., 70, 25-37, (2002) Real algebraic sets, Topology of real algebraic varieties Topology, moduli and automorphisms of real algebraic 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 \(x^n+y^m+1=0\) uniruled variety; polynomial automorphisms; identity sets Jelonek, Z.: Irreducible identity sets for polynomial automorphisms. Math. Z.212, 601--617 (1993) Automorphisms of surfaces and higher-dimensional varieties, Picard-type theorems and generalizations for several complex variables, Rational and ruled surfaces, Polynomial rings and ideals; rings of integer-valued polynomials Irreducible identity sets for 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 \(x^n+y^m+1=0\) automorphisms of polynomial algebras; tame automorphisms; wild automorphisms; defining relations of group of tame automorphisms Umirbaev U. U., ''Defining relations of the tame automorphism group of polynomial algebras in three variables,'' J. Reine Angew. Math. (Crelles Journal), No. 600, 203--235 (2006). Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Actions of groups on commutative rings; invariant theory, Polynomials over commutative rings, Birational automorphisms, Cremona group and generalizations, Generators, relations, and presentations of groups, Representations of groups as automorphism groups of algebraic systems Defining relations of the tame automorphism group of polynomial algebras in three 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 \(x^n+y^m+1=0\) rationality; extension of ground field; quartic curve Global ground fields in algebraic geometry, Arithmetic ground fields for curves, Cubic and quartic Diophantine equations Algebraic points on quartic curves 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 \(x^n+y^m+1=0\) number of automorphisms; minimal algebraic surfaces of general type; Hurwitz theorem {G. Xiao, } {Bound of automorphisms of surfaces of general type. I, } \textit{Ann. of Math.} \textbf{139} (1994), 51--77 Automorphisms of surfaces and higher-dimensional varieties, Surfaces of general type, Singularities of surfaces or higher-dimensional varieties Bound of automorphisms of surfaces of general 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 \(x^n+y^m+1=0\) derivation on the function field; divisor class group A. Buium, ?Class groups and differential function fields,? J. Algebra,89, No. 1, 56?64 (1984). Varieties and morphisms, Differential algebra, Morphisms of commutative rings, Iwasawa theory Class groups and differential 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 \(x^n+y^m+1=0\) Mukai, S.; Ohashi, H., Recent advances in algebraic geometry, The automorphism groups of Enriques surfaces covered by symmetric quartic surfaces, 307-320, (2015), Cambridge Univ. Press: Cambridge Univ. Press, Cambridge Automorphisms of surfaces and higher-dimensional varieties, \(K3\) surfaces and Enriques surfaces The automorphism group of Enriques surfaces covered by symmetric quartic 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 \(x^n+y^m+1=0\) Biswas, I.; Holla, Y. I., Brauer group of moduli of principal bundles over a curve, J. Reine Angew. Math., 677, 225-249, (2013) Vector bundles on curves and their moduli, Brauer groups of schemes Brauer group of moduli of principal bundles over a 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 \(x^n+y^m+1=0\) projective curve; sectional monodromy group; rational curve Plane and space curves, Coverings in algebraic geometry, Separable extensions, Galois theory Sectional monodromy groups of projective 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 \(x^n+y^m+1=0\) \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Geometric methods (including applications of algebraic geometry) applied to coding theory, Riemann surfaces; Weierstrass points; gap sequences, Computational aspects of algebraic curves Elementary abelian \(p\)-extensions of algebraic 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 \(x^n+y^m+1=0\) character theory 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. 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 \(x^n+y^m+1=0\) automorphism groups of affine varieties; ind-groups; Lie algebras of ind-groups When is the automorphism group of an affine variety nested?

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 surfaces and higher-dimensional varieties, Surfaces of general type Automorphisms of an irregular surface of general type acting trivially in cohomology. III

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 curve in general position; polynomial automorphisms Jelonek, Z.: Sets determining polynomial automorphisms of \(\mathbb{C}\)2. Bull. Acad. Pol. Math.37, no. 1-6 (1989) Automorphisms of curves, Polynomial rings and ideals; rings of integer-valued polynomials, Holomorphic mappings and correspondences Sets determining polynomial 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 \(x^n+y^m+1=0\) Prüfer v-multiplication domain; integral domain; Picard group; local class group; \(D+M\) construction D.F. Anderson and A. Ryckaert, The class group of \(D+M\), J. Pure Appl. Alg. 52 (1988), 199--212. Theory of modules and ideals in commutative rings, Extension theory of commutative rings, Divisibility and factorizations in commutative rings, Integral domains, Picard groups, Dedekind, Prüfer, Krull and Mori rings and their generalizations The class group of \(D+M\)

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 \(x^n+y^m+1=0\) Riemann surface; conformal automorphisms; anticonformal automorphisms Costa, A. F.; Porta, A. M.: Visualizing automorphisms of Riemann surfaces. Atti semin. Mat. fis. Univ. modena reggio emilia 58, 121-127 (2011) Riemann surfaces, Automorphisms of curves Visualizing automorphisms 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 \(x^n+y^m+1=0\) affine Cremona group; tame automorphism Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Birational automorphisms, Cremona group and generalizations Bitriangular polynomial automorphisms of affine spaces \(A_n\).

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; rational points; maximal curves; function fields Bassa, A.; Ma, L.; Xing, C.; Yeo, S. L., Toward a characterization of subfields of the Deligne-Lusztig function fields, \textit{J. Comb. Theory Ser. A}, 120, 1351-1371, (2013) Combinatorial aspects of representation theory, Curves over finite and local fields, Finite ground fields in algebraic geometry, Automorphisms of curves, Arithmetic theory of algebraic function fields Towards a characterization of subfields of the Deligne-Lusztig 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 \(x^n+y^m+1=0\) real cubic curves; automorphisms; classification Families, moduli of curves (algebraic), Real algebraic sets, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Automorphisms of curves An automorphic classification of real cubic 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 \(x^n+y^m+1=0\) moduli; hyperelliptic curves; Picard group Cornalba, M., The Picard group of the moduli stack of stable hyperelliptic curves, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 18, 1, 109-115, (2007) Families, moduli of curves (algebraic), Algebraic moduli problems, moduli of vector bundles, Picard groups, Vector bundles on curves and their moduli The Picard group of the moduli stack of stable 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 \(x^n+y^m+1=0\) homogeneous Stein manifold; holomorphic automorphism group Deng, F; Zhou, X, Rigidity of automorphism groups of invariant domains in homogeneous Stein spaces, Izv. Ross. Akad. Nauk, Ser. Mat., 78, 37-64, (2014) Group actions on varieties or schemes (quotients), General properties and structure of complex Lie groups, Stein spaces, Homogeneous complex manifolds, Stein manifolds, Differential geometry of homogeneous manifolds Rigidity of automorphism groups of invariant domains in homogeneous Stein 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 \(x^n+y^m+1=0\) positive characteristic; Jordan property; algebraic group Birational automorphisms, Cremona group and generalizations, Group schemes, Linear algebraic groups over arbitrary fields, Automorphisms of surfaces and higher-dimensional varieties, Group actions on varieties or schemes (quotients), Positive characteristic ground fields in algebraic geometry Jordan property for algebraic groups and automorphism groups of projective varieties in arbitrary characteristic

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 \(x^n+y^m+1=0\) pseudo-real Riemann surface; field of moduli; field of definition; plane curve; automorphism group Plane and space curves, Automorphisms of curves, Compact Riemann surfaces and uniformization, Families, moduli of curves (algebraic) A class of pseudo-real Riemann surfaces with diagonal automorphism group

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; cubic threefolds; hypersurfaces; finite groups Automorphisms of surfaces and higher-dimensional varieties, Fano varieties, Hypersurfaces and algebraic geometry, Structure and classification of infinite or finite groups Automorphism groups of smooth cubic threefolds

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 curves; fundamental group; bifurcation graph; monodromy; Zariski-van Kampen's pencil method Coverings of curves, fundamental group, Singularities of curves, local rings, Special algebraic curves and curves of low genus, Plane and space curves On the fundamental groups of non-generic \(\mathbb R\) -join-type 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 geometry; symmetric products of curves; semistable degeneration; homotopy groups Surfaces of general type, Fibrations, degenerations in algebraic geometry, Homotopy groups of special spaces The fundamental group of the open symmetric product of a hyperelliptic 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 \(x^n+y^m+1=0\) curve singularity; algebraic fundamental group; arbitrary characteristic; power series ring Cutkosky, S. D.; Srinivasan, H.: The algebraic fundamental group of a curve singularity. J. algebra 230, 101-126 (2000) Coverings of curves, fundamental group, Singularities of curves, local rings, Formal power series rings, Algebraic functions and function fields in algebraic geometry, Germs of analytic sets, local parametrization, Homotopy theory and fundamental groups in algebraic geometry The algebraic fundamental group of a curve singularity

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 \(x^n+y^m+1=0\) hypergeometric series; field of automorphic functions on the unit ball T. Terada , Fonction hypergéométriques F1 et fonctions automorphes I , J. Math. Soc. Japan 35 (1983), 451-475; II, ibid. 37 (1985), 173-185. Automorphic functions in symmetric domains, Classical hypergeometric functions, \({}_2F_1\), Theta series; Weil representation; theta correspondences, General theory of automorphic functions of several complex variables, Linear algebraic groups over global fields and their integers, Families, moduli of curves (algebraic) Fonctions hypergéométriques \(F_ 1\) et fonctions automorphes. II: Groupes discontinus arithmétiquement définis

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 \(x^n+y^m+1=0\) Prym-Tjurin varieties; Schottky problem; principally olarized abelian variety; automorphism of curve; cyclic covering Theta functions and curves; Schottky problem, Automorphisms of curves, Jacobians, Prym varieties, Coverings of curves, fundamental group, Picard schemes, higher Jacobians Prym varieties of curves with an automorphism of prime order

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 fields; elliptic curves; cryptography M. R. Murty and I. E. Shparlinski, Group structure of elliptic curves over finite fields and applications, in Topics in Geometry, Coding Theory and Cryptography, Springer-Verlag, 2006, to appear. Curves over finite and local fields, Finite ground fields in algebraic geometry, Applications to coding theory and cryptography of arithmetic geometry, Algebraic coding theory; cryptography (number-theoretic aspects) Group structure of elliptic curves over finite fields and 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 \(x^n+y^m+1=0\) Birational automorphisms, Cremona group and generalizations, Real algebraic sets, Automorphisms of surfaces and higher-dimensional varieties \(p\)-subgroups in automorphism groups of real del Pezzo 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 \(x^n+y^m+1=0\) rational map; field of definition; moduli field Hidalgo, Rubén A., A simple remark on the field of moduli of rational maps, Q. J. Math., 65, 2, 627-635, (2014) Algebraic functions and function fields in algebraic geometry, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization), Rational and birational maps, Coverings of curves, fundamental group, Families, moduli of curves (algebraic) A simple remark on the field of moduli of rational 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 \(x^n+y^m+1=0\) DOI: 10.1007/s00574-004-0008-9 Algebraic functions and function fields in algebraic geometry, Arithmetic theory of algebraic function fields, Thue-Mahler equations, Finite ground fields in algebraic geometry On towers of function fields of Artin-Schreier 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 \(x^n+y^m+1=0\) complements of branch curves; fundamental group; moduli space of surfaces of general type; Veronese surface B. Moishezon and M. Teicher, Fundamental groups of complements of branch curves as solvable groups, in Proceedings of the Hirzebruch 65 Conference on Algebraic Geometry (Ramat Gan, 1993) Israel Mathematics Conference Proceedings (AMS Publications), vol. 9, 1996, pp. 329--346. Homotopy theory and fundamental groups in algebraic geometry, Surfaces of general type, Fundamental groups and their automorphisms (group-theoretic aspects) Fundamental groups of complements of branch curves as solvable 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 \(x^n+y^m+1=0\) Mordell-Weil rank; abelian variety; function field; Prym variety; Jacobian variety Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Jacobians, Prym varieties The rational points on certain abelian varieties 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 \(x^n+y^m+1=0\) Bibliography; enumeration of algebraic curves; enumeration of rational curves; string theory R. Piene, On the enumeration of algebraic curves--from circles to instantons, in First European Congress of Mathematics, Vol. II (Paris, 1992), pp. 327--353, Progr. Math., 120, Birkhäuser, Basel, 1994. Enumerative problems (combinatorial problems) in algebraic geometry, Special algebraic curves and curves of low genus On the enumeration of algebraic curves -- from circles to instantons

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 \(x^n+y^m+1=0\) Grassmannian; fundamental theorem of projective spaces; collineation M. Pankov, ''Transformations of Grassmannians and automorphisms of classical groups,'' J. Geom. 75 (2002), 132--150. Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations), Grassmannians, Schubert varieties, flag manifolds Transformations of Grassmannians and automorphisms of classical 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 \(x^n+y^m+1=0\) compact Riemann surface; automorphism group; splitting of the polarized Jacobian variety; group action -, The splitting of some Jacobi varieties using their automorphism groups, preprint. Jacobians, Prym varieties, Group actions on varieties or schemes (quotients), Riemann surfaces; Weierstrass points; gap sequences, Compact Riemann surfaces and uniformization The splitting of some Jacobi varieties using their automorphism 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 \(x^n+y^m+1=0\) automorphisms of surfaces of general type; positive characteristic J. Cai, ''Bounds of automorphisms of surfaces of general type in positive characteristic,'' J. Pure Appl. Algebra, vol. 149, iss. 3, pp. 241-250, 2000. Automorphisms of surfaces and higher-dimensional varieties, Surfaces of general type, Finite ground fields in algebraic geometry Bounds of automorphisms of surfaces of general type in positive characteristic

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 Cremona group; automorphism of the affine space; tame automorphisms Group actions on affine varieties, Birational automorphisms, Cremona group and generalizations An arbitrary nonlinear automorphism of the affine space \(A^3\) with the affine group generate the group of the tame automorphisms \(A^3\)

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 \(x^n+y^m+1=0\) Motivic cohomology; motivic homotopy theory, Stable homotopy theory, spectra On the zeroth stable \(\mathbb{A}^1\)-homotopy group of a smooth 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 \(x^n+y^m+1=0\) Weierstrass \(n\)-semigroup; smooth curve; semigroup of non-gaps Riemann surfaces; Weierstrass points; gap sequences On the Weierstrass semigroups of \(n\) points of a smooth curve: an addendum

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 \(x^n+y^m+1=0\) A trichotomy for the autoequivalence groups on smooth projective 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 \(x^n+y^m+1=0\) number of automorphisms of a nonsingular projective algebraic surface; classification of singular rational surfaces G. Xiao, \textit{Bound of automorphisms of surfaces of general type}, II, J. Algebraic Geom. 4 (1995), no. 4, 701-793. Automorphisms of curves, Automorphisms of surfaces and higher-dimensional varieties Bound of automorphisms of surfaces of general type. 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 \(x^n+y^m+1=0\) automorphisms of a generic Jacobian Kummer surface; Picard lattice Keum J H 1997 Automorphisms of Jacobian Kummer surfaces \textit{Compos. Math.}107 269--88 \(K3\) surfaces and Enriques surfaces, Automorphisms of surfaces and higher-dimensional varieties Automorphisms of Jacobian Kummer 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 \(x^n+y^m+1=0\) regular \({\mathbb{C}}^*\)-actions; normal forms of curves; Euler characteristic; characterization of the affine plane M. Zaidenberg, Rational actions of the group \(\mathbf{C}^{*}\) on \(\mathbf{C}^{2}\), their quasi-invariants, and algebraic curves in \(\mathbf{C}^{2}\) with Euler characteristic 1, Soviet Math. Dokl. 31 (1985), 57-60. Group actions on varieties or schemes (quotients), Families, moduli, classification: algebraic theory, Rational and birational maps, Complex Lie groups, group actions on complex spaces Rational actions of the group \({\mathbb{C}}^*\) on \({\mathbb{C}}^ 2\), their quasi-invariants, and algebraic curves in \({\mathbb{C}}^ 2\) with Euler characteristic 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 \(x^n+y^m+1=0\) rigid geometry; discontinuous groups; Mumford curves; Mumford groups; amalgams; orbifolds; stratified bundles Automorphisms of curves, Groups acting on trees, Rigid analytic geometry, Non-Archimedean function theory Mumford curves and Mumford groups in positive characteristic

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 \(x^n+y^m+1=0\) ------, The fundamental group of the complement of the branch curve of the surface \(T\times T,\) Osaka J. Math. 40 (2003), 1--37. Homotopy theory and fundamental groups in algebraic geometry, Fibrations, degenerations in algebraic geometry The fundamental group of the complement of the branch curve of \(T\times T\) 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 \(x^n+y^m+1=0\) Lüroth semigroup; plane curve; curve over a finite field; non-algebraically closed field Plane and space curves, Global ground fields in algebraic geometry The Lüroth semigroups of a curve over a non-algebraically closed 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 \(x^n+y^m+1=0\) birational automorphisms Birational automorphisms, Cremona group and generalizations Birational automorphisms of algebraic 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 \(x^n+y^m+1=0\) absolute Galois group; Shafarevich's conjecture; free profinite group; quasi-free profinite group; function field; real closed field; Laurent series field Harbater, D., On function fields with free absolute Galois groups, Journal für die Reine und Angewandte Mathematik, 632, 85-103, (2009) Inverse Galois theory, Separable extensions, Galois theory, Coverings of curves, fundamental group, Limits, profinite groups, Field arithmetic On function fields with free absolute Galois 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 \(x^n+y^m+1=0\) hypersurfaces; polynomial automorphism identity sets Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Polynomial rings and ideals; rings of integer-valued polynomials, Polynomials over commutative rings, Hypersurfaces and algebraic geometry, Morphisms of commutative rings, Automorphism groups of \(\mathbb{C}^n\) and affine manifolds On polynomial automorphism identity sets and identity polynomials

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 Cai J. (1995). On abelian automorphism groups of threefolds of general type. Algebra Colloq. 2(4): 373--382 Automorphisms of curves, \(3\)-folds, Automorphisms of surfaces and higher-dimensional varieties On abelian automorphism groups of 3-folds 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 \(x^n+y^m+1=0\) moduli space; Riemann surfaces; rational homology; Teichmüller space; mapping class group Harer J.L.: The third homology group of the moduli space of curves. Duke Math. J. 63(1), 25--55 (1991) General low-dimensional topology, Curves in algebraic geometry The third homology group of the moduli space 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 \(x^n+y^m+1=0\) linearization; polynomial automorphisms; hyperbolicity Envelopes of holomorphy About the linearization of certain subgroups of polynomial diffeomorphisms of the plane and the envelopes of holomorphy

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 \(x^n+y^m+1=0\) monodromy; moduli space of curves with level structure R. Hain: Monodromy of codimension-one sub-families of universal curves, arXiv:1006.3785. Structure of families (Picard-Lefschetz, monodromy, etc.), Homotopy theory and fundamental groups in algebraic geometry, Topological properties in algebraic geometry Monodromy of codimension 1 subfamilies of universal 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 \(x^n+y^m+1=0\) elliptic curves over number and finite fields; elliptic cryptography Curves over finite and local fields, Elliptic curves over global fields, Arithmetic ground fields for curves Parametric families of elliptic curves with cyclic \(\mathbb F_p\)-rational points 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 \(x^n+y^m+1=0\) automorphisms; dessins d'enfants Automorphisms of curves, Dessins d'enfants theory, Fuchsian groups and their generalizations (group-theoretic aspects), Geometric structures on manifolds of high or arbitrary dimension Groups as automorphisms of dessins d'enfants

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 \(x^n+y^m+1=0\) symmetric product of compact Riemann surface; fibrations; geometrical Brauer group Brauer groups of schemes, Families, moduli of curves (analytic), Classical real and complex (co)homology in algebraic geometry Brauer group of fibrations and symmetric products 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 \(x^n+y^m+1=0\) toric variety; automorphisms; flexible variety; rigid variety Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Toric varieties, Newton polyhedra, Okounkov bodies, Automorphisms of surfaces and higher-dimensional varieties Automorphisms of nonnormal toric 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 \(x^n+y^m+1=0\) general algebraic surface in complex 3-space; identity set for polynomials; polynomial automorphisms; generic surface Automorphisms of surfaces and higher-dimensional varieties, Power series, series of functions of several complex variables Sets determining polynomial automorphisms of \(\mathbb{C}{}^ 3\)

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; Weierstrass points; gap sequences, Automorphisms of curves, Classification theory of Riemann surfaces, Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) Group action on genus 7 curves and their Weierstrass points

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 \(x^n+y^m+1=0\) conjugacy classes; groups of triangular automorphisms; affine spaces; Jonquière groups; classes of maximal order; Sylow subgroups of symmetric groups Finite automorphism groups of algebraic, geometric, or combinatorial structures, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, Arithmetic and combinatorial problems involving abstract finite groups The conjugacy classes of the group of triangular automorphisms of affine space over a finite prime 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 \(x^n+y^m+1=0\) elliptic curves; \(\mathbb{Q}\)-curves; isogenies Elliptic curves over global fields, Elliptic curves \(\mathbb{Q}\)-curves over odd degree number 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 and surface; rank; torsion subgroup Elliptic curves over global fields, Elliptic curves On the family of elliptic curves \(X + 1/X + Y + 1/Y + t = 0\)

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 \(x^n+y^m+1=0\) automorphic form; definite quaternion algebra; Eichler-Shimura relation DOI: 10.4153/CJM-2001-005-5 Complex multiplication and moduli of abelian varieties, Modular and Shimura varieties, Galois representations On the curves associated to certain rings of automorphic forms

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 \(x^n+y^m+1=0\) extendability of an isomorphism of two affine subvarieties; polynomial automorphism S. Kaliman, \textit{Extensions of isomorphisms of subvarieties in flexible manifolds}, arXiv:1703.08461v6. Automorphisms of curves, Polynomial rings and ideals; rings of integer-valued polynomials, Analytic subsets of affine space Extensions of isomorphisms between affine algebraic subvarieties of \(k^ n\) to automorphisms of \(k^ n\)

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 \(x^n+y^m+1=0\) A. Fujiki: Automorphism groups of Joyce twistor spaces , preprint (2012). Twistor methods in differential geometry, Automorphisms of surfaces and higher-dimensional varieties, Compact complex \(3\)-folds, Twistor theory, double fibrations (complex-analytic aspects) Automorphism groups of Joyce twistor 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 \(x^n+y^m+1=0\) hyperelliptic curves; Galois descent; field of definition; field of moduli Grothendieck, A.: Techniques de construction et théorèmes d'existence en géométrie algébrique IV: les schémas de Hilbert. In: Séminaire Bourbaki. vol. 6, no.221, 249-276 . Soc. Math. France, Paris (1995) Computational aspects of algebraic curves, Actions of groups on commutative rings; invariant theory, Families, moduli of curves (algebraic), Arithmetic ground fields for curves, Automorphisms of curves Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group

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; Jacobian conjecture Fornæss, J.; Wu, H., Classification of degree 2 polynomial automorphisms of \(\mathbb C^3\), Publ. Mat., 42, 195-210, (1998) Holomorphic maps on manifolds, Automorphisms of curves Classification of degree 2 polynomial automorphisms of \(\mathbb{C}^3\)

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 \(x^n+y^m+1=0\) \(G\)-endomorphism; affine \(G\)-variety; algebraic quotient K. Masuda, G-endomorphisms of affine G-varieties which induce automorphisms of the invariant subrings of the coordinate rings, J. Algebra 307 (2007), no. 1, 97--105. Group actions on affine varieties, Group actions on varieties or schemes (quotients) \(G\)-endomorphisms of affine \(G\)-varieties which induce automorphisms of the invariant subrings of the coordinate rings

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 \(x^n+y^m+1=0\) hyperelliptic curve; class group Arithmetic theory of algebraic function fields, Class numbers, class groups, discriminants, Algebraic functions and function fields in algebraic geometry Fiber products and class groups of 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 \(x^n+y^m+1=0\) automorphism group; Mumford curve; normalizers of Schottky groups Cornelissen, G.; Kato, F., Mumford curves with maximal automorphism group II: Lamé type groups in genus 5-8, Geom. Dedicata, 102, 127-142, (2003) Automorphisms of curves, Rigid analytic geometry, Groups acting on trees Mumford curves with maximal automorphism group. II: Lamé type groups in genus 5-8

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 curve; unitary group; quotient curve; maximal curve; Wiman's sextic Automorphisms of curves, Curves over finite and local fields, Finite ground fields in algebraic geometry, Arithmetic ground fields for curves An \(\mathbb{F}_{p^2 } \)-maximal Wiman sextic and its 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 \(x^n+y^m+1=0\) algebraic fundamental group; affine curve; free profinite group; Abhyankar conjecture A. Pacheco, K.\ F. Stevenson and P. Zalesskii, Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic, Math. Ann. 343 (2009), no. 2, 463-486. Coverings of curves, fundamental group, Separable extensions, Galois theory, Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory), Homotopy theory and fundamental groups in algebraic geometry, Limits, profinite groups Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic

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 \(x^n+y^m+1=0\) commuting polynomial automorphisms; indeterminacy set; Hénon maps; Green functions; blow-up Bisi, C, On commuting polynomial automorphisms of \(C^k\), \(k### 3\), Math. Z., 258, 875-891, (2008) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets On commuting polynomial automorphisms of \({\mathbb{C}}^{k}\), \(k \geq 3\)

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 \(x^n+y^m+1=0\) triangle group; Fuchsian group; Lamé differential equation; Belyĭ maps; Picard-Fuchs type Vignéras, M.-F.: Arithmétique des algèbres de quaternions. In: Lecture Notes in Math, vol. 800. Springer, Berlin (1980) Dessins d'enfants theory, Modular and Shimura varieties, Computational aspects of algebraic curves, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) Arithmetic \((1;e)\)-curves and Belyĭ 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 \(x^n+y^m+1=0\) Singularities of surfaces or higher-dimensional varieties, Automorphisms of surfaces and higher-dimensional varieties, Homotopy theory and fundamental groups in algebraic geometry, Singularities in algebraic geometry Algebraic surfaces with quotient singularities -- including some discussion on automorphisms and 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 \(x^n+y^m+1=0\) division algebra over function field; sheaf of differentials; maximal order; Riemann-Roch theorem; genus M. van den Bergh and J. Van Geel, Algebraic elements in division algebras over function fields of curves, Israel J. Math., 52 (1985), no. 1-2, 33--45. Zbl 0596.12012 MR 0815599 Quaternion and other division algebras: arithmetic, zeta functions, Transcendental field extensions, Skew fields, division rings, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Arithmetic theory of algebraic function fields, Division rings and semisimple Artin rings, Algebraic functions and function fields in algebraic geometry Algebraic elements in division algebras over function fields 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 \(x^n+y^m+1=0\) threshold of canonical adjunction; birationally supervariety A.~V.~Pukhlikov 1998 Birational automorphisms of Fano hypersurfaces \textit{Invent. Math.}134 2 401--426 Birational automorphisms, Cremona group and generalizations, Hypersurfaces and algebraic geometry, Fano varieties, Rational and birational maps, Adjunction problems, Divisors, linear systems, invertible sheaves Birational automorphisms of Fano 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 \(x^n+y^m+1=0\) rational points; modular curves; elliptic curves Arithmetic aspects of modular and Shimura varieties, Complex multiplication and moduli of abelian varieties, Rational points, Elliptic curves over global fields Points on \(X_0^+(N)\) 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 \(x^n+y^m+1=0\) Weierstrass semigroup; maximal curve; AG code; Hermitian curve Computational aspects of algebraic curves, Linear codes (general theory) Weierstrass semigroup at \(m+1\) rational points in maximal curves which cannot be 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 \(x^n+y^m+1=0\) projective equivalences; \(\mu\)-bases; rational curves Computational aspects of algebraic curves, Computer-aided design (modeling of curves and surfaces), Computational methods for problems pertaining to geometry, Curves in algebraic geometry Using \(\mu \)-bases to reduce the degree in the computation of projective equivalences between rational curves in \(n\)-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 \(x^n+y^m+1=0\) curves; genus Di Gennaro, V.: Hierarchical structure of the family of curves with maximal genus verifying flag conditions. Proc. Amer. Math. Soc. (to appear) Plane and space curves, Projective techniques in algebraic geometry, Families, moduli of curves (algebraic), Classical problems, Schubert calculus Hierarchical structure of the family of curves with maximal genus verifying flag conditions

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; permutation groups; tame automorphism group S. Maubach, R. Willems, \textit{Polynomial automorphisms over finite fields: mimicking tame maps by the Derksen group}, Serdica Math. J. \textbf{37} (2011), no. 4, 305-322 (2012). Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Finite ground fields in algebraic geometry, Group actions on affine varieties, Infinite automorphism groups Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

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 \(x^n+y^m+1=0\) ground field extension; principally polarized Jacobian variety [23]K. Sekino and T. Sekiguchi, On the fields of definition for a curve and its Jacobian variety, Bull. Fac. Sci. Engrg. Chuo Univ. Ser. I Math. 31 (1988), 29--31. Jacobians, Prym varieties, Arithmetic problems in algebraic geometry; Diophantine geometry On the fields of definition for a curve and its Jacobian variety

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 \(x^n+y^m+1=0\) tame automorphism; multidegree; elementary reduction; arithmetic progression Li, J.; Du, X.: Tame automorphisms with multidegrees in the form of arithmetic progressions Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) Tame automorphisms with multidegrees in the form of arithmetic progressions

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 algebras; \(A_{\infty}\)-structure; Massey products; derived category; sheaves; Hochschild cohomology; algebraic curve; moduli of curves Fisette, R; Polishchuk, A, A\(_\infty \)-algebras associated with curves and rational functions on \({\fancyscript {M}}_{g, g}\). I, Compos. Math., 150, 621-667, (2014) Families, moduli of curves (algebraic), Differential graded algebras and applications (associative algebraic aspects), (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Massey products \(A_{\infty }\)-algebras associated with curves and rational functions on \(\mathcal{M}_{g,g}\). 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 \(x^n+y^m+1=0\) supergeometry; Lie theory; algebraic geometry Group actions on varieties or schemes (quotients), Supervarieties, Supermanifolds and graded manifolds The projective linear supergroup and the SUSY-preserving automorphisms of \(\mathbb{P}^{1|1}\)

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 \(x^n+y^m+1=0\) elliptic curve; Mordell-Weil group; generators; height function Elliptic curves over global fields, Elliptic curves Complete characterization of the Mordell-Weil group of some families of elliptic 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 \(x^n+y^m+1=0\) elliptic curves over finite fields; rational points Curves over finite and local fields, Arithmetic ground fields for curves, Finite ground fields in algebraic geometry The group structure of Bachet elliptic curves over finite fields \(\mathbb F_p\)

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 \(x^n+y^m+1=0\) Topology of real algebraic varieties, Jacobians, Prym varieties, Real algebraic sets A criterion for \(M\)-curves