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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. monomial curves; not set theoretic complete intersections DOI: 10.1080/00927879408824983
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. algebraic curve; transcendental analytic functions; number of rational points; height Pila, J., \textit{geometric postulation of a smooth function and the number of rational points}, Duke Math. J., 63, 449-463, (1991)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. star configuration; set-theoretic complete intersection
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. algebraic points; subvarieties; canonical height; nontrivial translates; torsion points; Lehmer's problem; points of minimal height E. Bombieri and U. Zannier, Algebraic points on subvarieties of \?\(^{n}\)_{\?}, Internat. Math. Res. Notices 7 (1995), 333 -- 347.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. ring of analytic function germ; Łojasiewicz exponent; integral closure of ideal; mixed multiplicities of an ideal; monomial ideal; Newton polyhedron
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. canonical sheaf; subcanonical curve; complete intersection [C-V]2 Chiantini L., Valabrega P.,Subcanonical curves and complete intersections in projective 3-space. Ann. Mat. Pura Appl. (1984) 309--330.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. finite-dimensional algebras; degenerations of modules; minimal degenerations; tame quasi-tilted algebras; representations of algebras; categories of modules Zwara, G.: Degenerations of finite-dimensional modules are given by extensions. Compos. Math. 121(2), 205--218 (2000)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. homogeneous manifold; Schubert variety; deformations; variety of minimal rational tangents Bourbaki, N.: Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris (1968)
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. canonical local height; elliptic curve; computation of the canonical global height Horst G. Zimmer, A limit formula for the canonical height of an elliptic curve and its application to height computations, Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp. 641 -- 659.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. sums of squares; complete intersection; unmixed surface germs; positive semi-definite function germ; mixed surface germs DOI: 10.1007/s00209-003-0519-x
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. almost set-theoretic complete intersection; affine toric variety; defining equations DOI: 10.1016/j.jpaa.2005.09.008
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. convex set; convex hull; irredundancy; linear matrix inequality; nonsingularity; positive curvature; semialgebraic set; semidefinite programming; semidefinite representation; (strictly) quasi-concavity; singularity; smoothness; sos-concavity; sum of squares J. W. Helton and J. Nie, \textit{Sufficient and necessary conditions for semidefinite representability of convex hulls and sets}, SIAM J. Optim., 20 (2009), pp. 759--791.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. simplicial cohomology theory of commutative algebras; complete intersection Avramov, L. L.: Local rings of finite simplical dimension. Bull. amer. Math. soc. (N.S.) 10, 289-291 (1984)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. homogeneous filling; exact \(k\)-filling of the euclidean \(m\)-space; smooth exact fillings; singular set
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. curve of almost minimal degree; minimal free resolution W. Lee and E. Park, Projective curves of degree=codimension+2 II. Internat. J. Algebra Comput. 26 (2016), no. 1, 95-104.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. monomial curves as set-theoretic complete intersections Thoma, A., On the set-theoretic complete intersection problem for monomial curves in A\textit{n} and \(\mathbb{P}\)\textit{n}, J. Pure Appl. Algebra, 104, 3, 333-344, (1995)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. \(X_ 1(N)\); modular elliptic curve of level N; parametrization; minimal Néron lattice; Stickelberger elements
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Lie-Rinehart algebra; Lie-Rinehart cohomology; quasi-homogeneous surface singularity; integrable connection; algebra of invariants; equivariant Lie-Rinehart cohomology
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. rational mapping; regular mapping; curve of genus one; quasi-group of rational points
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. equations defining space curves; complete linear system; integral curve; index of completeness L. Gruson, R. Lazarsfeld, C. Peskine, On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72(3), 491--506 (1983).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. decomposition of diagonal; Calabi-Yau complete intersection; decomposable 0-cycle; Chow ring; intersection theory; Hodge structure Fu, L, Decomposition of small diagonals and Chow rings of hypersurfaces and Calabi-Yau complete intersections, Adv. Math., 244, 894-924, (2013)
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. upper bounds for the number of singularities; deformation of an isolated complete intersection singularity
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. second fundamental form; complete intersection; field of rational functions
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. ideal of the affine cone of a curve; free resolution Amasaki M., Publ. RIMS 19 pp 493-- (1983)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. set theoretic complete intersection DOI: 10.1007/BF02568773
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. differential topology of complex surfaces; oriented smooth 4-manifold; canonical class; differential topological invariant; action of diffeomorphisms; moduli spaces of instantons; complex algebraic surfaces; minimal elliptic; complete intersections; homeomorphic but not diffeomorphic R. Friedman , B. Moishezon and J.W. Morgan : On the C\infty invariance of the canonical classes of certain algebraic surfaces . Bull. Amer. Math. Soc. (N.S.) 17 (1987) 283-286.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. monomial ideal; tetralhedral curve; liason; arithmetically Cohen-Macaulay Migliore, J; Nagel, U, Tetrahedral curves, Int. Math. Res. Not., 15, 899-939, (2005)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Macaulayfication; blow-up of algebraic varieties; normal torsion-free subvariety; tangent cones; n-jet; locally almost complete intersection Brodmann, M.: Blow-up and asymptotic depth of higher conormal modules. Preprint
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Hirzebruch l-homology class for compact oriented PL-pseudo-manifolds; intersection formula; strate of even codimension
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. generalized Weierstraß semigroup; complete intersection curve Delgado, F.: The symmetry of the Weierstrass generalized semigroups and affine embeddings. Proc. Am. Math. Soc. 108(3), 627--631 (1990)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection; Fano varieties; rational homogeneous varieties
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. adjacent ideals; base points of ideals; complete ideal; cluster of points; regular local ring; sandwiched surface singularities; weighted cluster; Zariski factorization Fernández-Sánchez, J.: Factorization of adjacent complete ideals in dimension 2, Proc. roy. Soc. Edinburgh sect. A 137, 913-921 (2007)
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. elliptic curve; prime of supersingular reduction DOI: 10.1007/BF02837827
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. rational normal curves; set-theoretic complete intersection; quadratic polynomials; Gröbner bases
0
quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. group generated by pseudo-reflections; ideal of generalized invariants; homogeneous elements; Chevalley-Shepard-Todd theorem; cohomology; twisted derivations; Kac-Moody groups; Lie algebra cohomology Victor G. Kac and Dale H. Peterson, Generalized invariants of groups generated by reflections, Geometry today (Rome, 1984) Progr. Math., vol. 60, Birkhäuser Boston, Boston, MA, 1985, pp. 231 -- 249.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complex affine curve; ring of differential operators; ad-nilpotent elements; ring of regular functions; injective birational map; invariants of simple rings; non-isomorphic curves with isomorphic rings of differential operators; codimension DOI: 10.1112/jlms/s2-45.1.17
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Auslander-Reiten quiver; germ of a normal complex surface singularity; isomorphism classes of vector bundles; reflexive modules; reduction cycle; rational singularities; minimal-elliptic singularities; simply- elliptic singularites; torsion free modules over plane curve singularities Kahn, Reflexive Moduln auf einfach-elliptischen Flächensingularitäten, Dissertation (1988)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. ideal class group; elliptic curve; Weierstrass class; semistable elliptic curves; minimal Weierstrass equation
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. surface singularities; 3-dimensional homology spheres; link of a complete intersection surface singularity; rational homology spheres Sell, On the topology of surface singularities {zn = f(x, y)}, for f irreducible, Michigan Math. J. 59 (1) pp 85-- (2010)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. proving geometrical theorems; triangular chain of polynomials; canonical triangular basis; polynomial ideal; quasialgebraic set; algebraically closed field Ko, H. P.: Geometry theorem proving by decomposition of quasi-algebraic sets: an application of the ritt-Wu principle. Artificial intelligence 37, 95-122 (1988)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. algebraic fundamental group of a complete irreducible non-singular algebraic curve
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete ideal; normal ideal of an affine domain; Rees algebra; \(S_ 2\); polynomial ring; hypersurface rings; almost complete intersections; computer algebra; Gröbner basis P. Brumatti, A. Simis and W. V. Vasconcelos, Normal Rees algebras, J. Algebra 112 (1988), 26--48.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Cohen-Macaulay semigroup; minimal system of generators for an ideal; triangular basis; lattice of relations Barile, M.; Morales, M.; Thoma, A.: On systems of relations associated to toric semigroups. Queen's papers in pure and appl. Math. 123, 173-185 (2002)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. curve consisting of linear systems; smooth complete curve; genus G. R. Kempf, Curves of {\(g^1_d\)}-s. \textit{Compositio Math.}\textbf{55} (1985), 157-162.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. semistable curve; moduli of curves; resolution of singularities; alteration; integral variety; monoidal transformations; semi-stable reduction theorem; multiplicity of intersection for two modules; Monsky-Washnitzer cohomology groups; monodromy actions on étale cohomology Berthelot, P., Altérations de variétés algébriques (d'après A.J. de jong), Séminaire Bourbaki, vol. 1995/96, Astérisque, 241, 273-311, (1997), Exp. No. 815, 5
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. torsionfree modules; finite Cohen-Macaulay type; complete local ring of a reduced curve singularity; finite CM type G.-M. Greuel and H. Knörrer, Einfache Kurvensingularitäten und torsionsfreie Moduln, Math. Ann. 270 (1985), no. 3, 417 -- 425 (German).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. split normal bundle; curve on surface; complete intersection Strømme S. A., Space curves (Rocca di Papa, 1985) pp 251-- (1987)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. enumeration of curves; complete linear system; plane curve singularities S.\ L. Kleiman and R. Piene, Enumerating singular curves on surfaces, Algebraic geometry: Hirzebruch 70 (Warsaw 1998), Contemp. Math. 241, American Mathematical Society, Providence (1999), 209-238.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. quadric curve; gaps; complete intersection curves; Cohen-Macaulay curves; Buchsbaum curves; Lüroth semigroup DOI: 10.1007/BF02567082
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. classification of quasi-homogeneous singularities; normal forms
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. arithmetical rank; monomial ideals; set-theoretic complete intersections; Stanley-Reisner ideals Barile, M.: Arithmetical ranks of Stanley--Reisner ideals via linear algebra. Preprint, math.AC/0703258
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. local cohomology modules; formal grade; set-theoretically and cohomologically complete intersection ideals; analytic spread; monomials Eghbali, M., On set theoretically and cohomologically complete intersection ideals, \textit{Canad. Math. Bull.}, 57, 3, 477-484, (2014)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. intersection theory; linear embeddings; ideal sheaves of linear type; Segre class Keel, S., Intersection theory of linear embeddings, Trans. Amer. Math. Soc., 335, 195-212, (1993)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. homological mirror symmetry; reflexive polytopes; Calabi-Yau complete intersection; Fano toric varities; derived category of coherent sheaves Favero, D., Kelly, T.L.: Proof of a conjecture of Batyrev and Nill. Am. J. Math. (2014). arXiv:1412.1354
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection; discriminant set; Horn hypergeometric function Tanabe, S., On horn--kapranov uniformisation of the discriminantal loci, Adv. Stud. Pure Math., 46, 223-249, (2007)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. face monoid; Kac-Moody group; buildings; homogeneous prime ideals of the Cartan algebra Mokler, C., An algebraic geometric model of an action of the face monoid associated to a Kac-Moody group on its building, J. pure appl. algebra, 219, 331-397, (2015)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. rings of differential operators; generic hyperplane arrangements; minimal free resolution; Jacobian ideal; jet modules
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. minimal free resolution; tangent bundle; Betti numbers; maximal rank; set of points in \(\mathbb{P}^n\); minimal resolution conjecture; Cohen-Macaulay type conjecture Lauze F., Manuscripta Math 92 pp 525-- (1997)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. homogeneous divisors; group actions; almost homogeneous variety; two- orbit variety; classification of complete normal two orbit surfaces D. Ahiezer, ''Equivariant completions of homogeneous algebraic varieties by homogeneous divisors,''Ann. Glob. Anal. Geom.,1, 49--78 (1983).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. log Hodge de Rham spectral sequences in finite characteristic; log Kodaira vanishing theorem in finite characteristic; log weak Lefschetz conjecture for log crystalline cohomologies; quasi-F-split height; log deformation theory with relative Frobenius; lifts of log smooth integral schemes over \(\mathcal{W}_2\)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. algebraic surfaces; intersection theory; singularities; ruled surfaces; quasielliptic fibrations; minimal model theory; canonical dimension; Enriques-Kodaira classification of algebraic surfaces; characteristic \(p\); elliptic fibrations; rational surfaces Bădescu, L., Algebraic surfaces, Universitext, (2001), Springer-Verlag New York, Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author. MR 1805816
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. linkage; complete intersection curve; Hilbert function; arithmetically Cohen-Macaulay curve; arithmetically Buchsbaum space curve
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. degree of a curve; intersection multiplicity; plane algebraic curve
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection; Cayley-Bacharach Theorem; zero-dimensional scheme; minimal distance; generalized Reed-Muller code A.V. Geramita and M. Kreuzer, On the uniformity of zero-dimensional complete intersections , J. Algebra 391 (2013), 82-92.
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection; smooth affine curve
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of \({\mathbb{C}}^*\)-type Kizuka T. , Rational functions of C \ast -type on the two-dimensional complex projective space , Tohoku Math. J. (2) 38 ( 1 ) ( 1986 ) 123 - 178 . Article | Zbl 0577.14021
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. tetrahedral curve; Alexander duality; arithmetically Cohen-Macaulay; monomial ideal; chordal graph; polarization; edge ideal; Stanley-Reisner ring DOI: 10.1016/j.jpaa.2007.05.017
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. representation growth; Igusa zeta function; points of schemes over finite ring; complete intersection; rational singularities; representation zeta function
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. irreducible complex algebraic curve; normalization map; rings of differential operators; monomial curves Letzter, G.; Makar-Limanov, L.: Rings of differential operators over rational affine curves. Bull. soc. Math. France 118, 193-209 (1990)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. curve singularity; conductor ideal; intersection number
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. codimension-one; faithfully flat; finite generation; retraction; complete local; Krull domain; divisorial ideal; symbolic power S.M. Bhatwadekar, Amartya K. Dutta and Nobuharu Onoda, On algebras which are locally \(\A^1\) in codimension-one , Trans. Amer. Math. Soc.,
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Segre class; zeta function; homogeneous ideal; ranks of a smooth variety; duality defect
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Rees algebra; \(S_ 2\); \((S_{k+1})\); complete intersection; Noetherian ring; canonical module; minimal extension; finite extension; Gorenstein local ring Noh, Sunsook; Vasconcelos, Wolmer V., The \(S_2\)-closure of a Rees algebra, Results Math., 23, 1-2, 149-162, (1993)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. sums of two cubes; Heegner points; elliptic curve; prime numbers
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. zero-dimensional ideal; border basis; border basis scheme; Cayley-Bacharach property; Gorenstein ring; strict complete intersection
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Gröbner basis for defining ideal; monomial curve Sengupta, I.: A Gröbner basis for certain affine monomial curves. Commun. Algebra 31(3), 1113--1129 (2003)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. minimal rational curves; analytic continuation; variety of minimal rational tangents; rational homogeneous manifold Hong, J; Mok, N, Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogenous manifolds, J Diff Geom, 86, 539-567, (2010)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. degree complexity; graded lexicographic order; generic initial ideal; partial elimination ideal; algebraic surfaces of codimension 2 Ahn, J; Kwak, S; Song, Y, The degree complexity of smooth surfaces of codimension 2, J. Symb. Comput., 47, 568-581, (2012)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Séminaire; Pinceaux arithmétiques; Mordell conjecture; modular height; effectiveness of bound for Mordell conjecture; proof of the Mordell conjecture; modular heights; isogenies; Tate conjecture; Shafarevich conjecture; intersection theory of Arakelov Szpiro, L. : Séminaire sur les pinceaux arithmétiques: la conjecture de Mordell , Astérisque 127, Soc. Math. de France (1985).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. completely integrable systems; topological structure of phase space; integration methods; Jacobians; Prym varieties; Hamiltonian systems; complete intersection Lesfari, A., Integrable systems and complex geometry. Lobachevskii Journal of Mathematics, Vol.30, No.4, 292-326 (2009).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. equisingularity; topological type of singularity; complete intersection isolated singularity; Milnor numbers; isomorphic monodromy fibrations Parameswaran, AJ, Topological equisingularity for isolated complete intersection singularities, Compos. Math., 80, 323-336, (1991)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. codimension two cycles; intermediate jacobian; complete intersection threefolds K. PARANJAPE , Curves on Threefolds with Trivial Canonical Bundle (Proc. Indian Acad. Sci. Math. vol. 101, 1991 , n^\circ 3, p. 199-213). MR 93a:14036 | Zbl 0759.14031
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Fano manifold; Campana-Peternell conjecture; rational homogeneous manifold; rational curve of degrees \(\leq 3\); Hermitian-Einstein metrics Hwang, J.M.: Rigidity of rational homogeneous spaces. In: Sanz-Solé, M., Soria, J., Varona, J.L., Verdera, J. (eds.) International Congress of Mathematicians, vol. II, pp. 613-626. European Mathematical Society, Zürich (2006)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. section of the Grassmannian; curve as intersection; restriction of an automorphism Shigeru Mukai, ``Curves and symmetric spaces, I.'', Am. J. Math.117 (1995) no. 6, p. 1627-1644
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. abelian gauged linear sigma model; Landau-Ginzburg model; conformal field theory; Berry phase; maximally unipotent monodromy; homological projective duality; non-commutative space; Calabi-Yau; Fano; discrete torsion; stack; complete intersection; Clemens double octic; McKay correspondence; moduli space of vector bundles on complete intersection of quadrics Căldăraru, A.; Distler, J.; Hellerman, S.; Pantev, T.; Sharpe, E., Non-birational twisted derived equivalences in abelian glsms, Commun. Math. Phys., 294, 605, (2010)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. minimal degree of a surface containing a closed integral curve
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Chow group; vanishing of intersection multiplicity; complete intersection; local Chern characters
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. germ of a holomorphic mapping; complete intersection; isolated singularity; Milnor number; regular fibre Pickl, A.,Die Homologie der Einhängung eines vollständigen Durchschnitts mit isolierter Singularität. Diplomarbeit, Regensburg (1983).
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. singular curve; adjoint ideal; linear series; saturated homogeneous; ideal; normalization CHIARLI,N.:?Completeness and Non-Speciality of Linear Series on Space Curves and Deficiency of the Corresponding Linear Series on Normalization?, Ann. di Mat.pura e appl.(IV), Vol. CXLI (1985) 177-186
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. Noether-Lefschetz theorem; curve contained in a general three-fold; complete intersection Wu X.: On a conjecture of Griffiths-Harris generalizing the Noether-Lefschetz theorem. Duke Math. J. 60(2), 465--472 (1990)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. geometric genus; weighted dual graphs of minimally elliptic complete intersection singularities
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. depth; regularity; monomial ideal; powers of an ideal; edge ideal; very well-covered graph; chordal graph
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. cone structures; rational homogeneous space; varieties of minimal rational tangents; Cartan connections; parabolic geometry; filtered manifolds
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. desingularization; germs of vector fields; quasi-homogeneous blowing ups Pelletier, M.: Eclatements quasi-homogènes. (1992)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. complete intersection of three quadrics; intermediate Jacobian; principally polarized abelian variety; Prym variety
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. cohomology; Witt ring of elliptic curve; symmetric bilinear spaces; algebraic scheme; complete regular curve Arason, Jón Kr.; Elman, Richard; Jacob, Bill: On generators for the Witt ring, Contemp. math. 155, 247-269 (1994)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of; \({\mathbb{C}}^*\)-type Kizuka, T.: Rational functions of ?*-type on the two-dimensional complex projective space. Tôhoku Math. J. 38, 123-178 (1986)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. minimal model of the Fermat curve; regular model; resolution of singularities
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. defining the set of integers; discrete set; real field; expansions of subfields; cyclic multiplicative subgroups; definably complete expansion; Baire category theorem Hieronymi, Philipp, Expansions of subfields of the real field by a discrete set, Fund. Math., 215, 2, 167-175, (2011)
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quasi-complete intersection; monomial curve; codimension 2; minimal generating set; homogeneous prime ideal of height 2 H. Bresinsky, P. Schenzel, and J. Stückrad, Quasi-complete intersection ideals of height 2, J. Pure Appl. Algebra 127 (1998), no. 2, 137 -- 145. asymptotic rank of an elliptic curve; Néron-Tate height of basis points of the Mordell-Weil group
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