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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. Euler characteristic; semi-algebraic set; complete intersection Dutertre, N.: An algebraic formula for the Euler characteristic of some semi-algebraic sets. J. pure appl. Algebra 139, 41-60 (1999)
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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 bases; polynomial ideal; noetherian ring; standard bases; open set of flatness of Spec Assi, A.: On flatness of generic projections. J. symbolic comput. 18, No. 5, 447-462 (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. purity of branch locus; regular local ring; complete intersection 7. Cutkosky, Steven Dale Purity of the branch locus and Lefschetz theorems Compos. math.96 (1995) 173--195 Math Reviews MR1326711
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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. filtration in the automorphism group; fundamental group of a smooth irreducible complete curve Oda, T.: A note on ramification of the Galois representation on the fundamental group of an algebraic curve. J. number theory 34, 225-228 (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. braid monodromy; plane algebraic curve; hyperplane arrangement; fundamental group of the complement of an algebraic curve; polynomial cover; braid group; wiring diagram; intersection lattice Daniel C. Cohen, Alexander I. Suciu, The braid monodromy of plane algebraic curves and hyperplane arrangements, Comment. Math. Helv. 72 (1997), 285-315 Zbl0959.52018 MR1470093
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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. Arakelov intersection theory; resolution of singularities; Green currents; complete intersections; zeta-integral; heights of arithmetic cycles Berenstein C., Yger A.: Green currents and analytic continuation. J. Anal. Math. 75, 1--50 (1998)
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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 number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension
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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 two plane curves; Hilbert function of a \(0\)- cycle D. S. Sodhi, ``Ice-induced vibrations of structures,'' Special Report 89-5, International Association for Hydraulic Research Working Group on Ice Forces, 1989.
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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. Colmez conjecture; complex multiplication; \(L\)-function; Faltings height; arithmetic intersection; Shimura 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. Mori's minimal model program; classification of projective n-folds; numerical positivity; canonical bundle; nef; extremal ray; terminal singularities; flips; vanishing; base-point freeness; rationality; harmonic maps; variations of Hodge structures; complete intersections; general type; terminal varieties; canonical singularities; extremal neighborhoods Clemens, H.; Kollár, J., Higher-dimensional complex geometry, Astérisque, 166, (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. smooth manifold; algebraic set; isotopy; complete intersection; vector bundle
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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 points; unions of lines; homogeneous coordinate rings; Hilbert function Les Reid and Leslie G. Roberts, Intersection points of seminormal configurations of lines, Algebraic \?-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989) Contemp. Math., vol. 126, Amer. Math. Soc., Providence, RI, 1992, pp. 151 -- 163.
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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. graded rings and algebras; derivations; quasihomogeneous singularities; isolated complete intersection singularities; graded Gorenstein singularities; quotient singularities; derivations of negative weight
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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. flattening stratification; modular deformation; modular deformations of isolated complete intersection singularities; singular B. Martin, ''Algorithmic computation of flattenings and of modular deformations, J. Symbol. Comput., 34, No. 3, 199--212 (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. Cohen-Macaulay coordinate ring; normal homogeneous coordinate ring; flag variety; unipotent transformatin; tableaus; Young diagram; fixed point subvarieties of the Schubert cells; minimal unipotent variety Shimomura, N., The fixed point subvarieties of unipotent transformations on the flag varieties, J. Math. Soc. Japan, 37, 3, 537-556, (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. complete curve; complete valued field; uniformization of the Jacobian variety J. Fresnel and M. Van der Put, Uniformisation de variétés de Jacobi et déformations de courbes, Annales de la Faculté des Sciences de Toulouse 3 (1994), 363--386.
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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. primitive length of a smooth curve; complete linear series; Clifford sequence 3. Coppens, M., Keem, C., Martens, G.: Primitive linear series on curves. Manuscripta Math. \textbf{77}, 237-264 (1992)CKM
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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. Milnor number of an isolated complete intersection singularity; Newton polyhedron Hamm, H.A.: Differential forms and Hodge numbers for toric complete intersections. arXiv:1106.1826
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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. nonsingular complete intersection; number of points; projective complete intersection; finite field; Deligne's theorem Hooley C.: On the number of points on a complete intersection over a finite field. Journal of Number Theory 38, 338--358 (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. quasi-homogeneous hypersurfaces; torsion module of differential module Ruth I. Michler, On the number of generators of the torsion module of differentials, Proc. Amer. Math. Soc. 129 (2001), no. 3, 639 -- 646.
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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 approach to Eichler's arithmetic theory of definite quaternion algebras; modular forms of weight 3/2; Waldspurger's formula; elliptic curves with prime conductor; critical values of L-series; weight two cusp form; special points; height pairing B. H. Gross, ''Heights and the special values of \(L\)-series,'' in Number Theory, Providence, RI: Amer. Math. Soc., 1987, vol. 7, pp. 115-187.
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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. Lie groups of rank one; reductive complex linear algebraic group; finite- dimensional complex representation; coregular representation; invariant polynomials; complete intersection; maximal torus; complete cointersection; fundamental representations; irreducible representations; highest weights Haruhisa Nakajima, ?Invariants of reductive Lie groups of rank one and their applications,? Proc. Japan Acad.,A60, No. 6, 221?224 (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. polynomial invariants; Poincaré series; Hironaka decomposition; minimal set of generators {\Dsstroke}oković, DŽ, On orthogonal and special orthogonal invariants of a single matrix of small order, Linear Multilinear Algebra, 57, 4, 345-354, (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. smooth complete complex algebraic variety; complex affine algebraic group; dense orbit; homogeneous divisors; compact isotropic Riemannian homogeneous space; embedding theory of spherical homogeneous spaces M. Brion,On spherical varieties of rank one, CMS Conf. Proc.10 (1989), 31--41.
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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. Frobenius classes; volumes of tubes; semi-algebraic set; prime number theorem in algebraic number fields; Chebotarev's density theorem; equidistribution of prime ideals B. Z. Moroz, ''Equidistribution of Frobenius classes and the volumes of tubes,'' Acta Arith., 51, 269--276 (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. implicitization; Gröbner basis; implicit ideal for a set of rational parametric equations X. S. Gao and S. C. Chou, Implicitization of rational parametric equations, Journal of Symbolic Computation, 1992, 14(5): 459--470.
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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. holomorphic functions of finite growth order; 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. prime ideal in the ring of semialgebraic functions; Krull dimension Gamboa, On prime ideals in rings of semialgebraic functions, Proc. Amer. Math. Soc. 118 (4) pp 1034-- (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. degree of a point; arithmetically Cohen-Macaulay curve; variety of minimal degree L. Bazzotti and M. Casanellas, Separators of points on algebraic surfaces,J. Pure Appl. Algebra 207 (2006), 319--326.
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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. growth functions; formal moduli space; complete topological modules; completion of the local ring of a plane curve singularity; convergence of formal power series in noncommuting variables
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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 Lucian Bădescu and Giuseppe Valla, Grothendieck-Lefschetz theory, set-theoretic complete intersections and rational normal scrolls, J. Algebra 324 (2010), no. 7, 1636 -- 1655.
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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 syzygies; degree of a minimal set of defining equations; fat points; Castelnuovo-Mumford regularity Hà, Huy Tài; Van Tuyl, A.: The regularity of points in multi-projective spaces. J. pure appl. Algebra 187, No. 1 -- 3, 153-167 (2004)
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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. plane curve germ; Newton diagram; equivalence of terms; strong triangle inequality; quasi-branch
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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. \(p\)-adic height pairings; elliptic curve; Iwasawa theory; supersingular reduction; Hodge filtration of the Dieudonné module; formal group Plater, A.: Supersingular p-adic height pairings on elliptic curves. In: Arithmetic Geometry, Tempe, AZ, 1993. Contemp. Math., vol. 174, pp. 95--105. Am. Math. Soc., Providence (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. set-theoretic complete intersection; arithmetical rank DOI: 10.1006/jabr.1999.8195
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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. a hyperbolic projective variety is Mordellic; rational points; exceptional set; algebraic characterization of hyperbolicity; Chern-Ricci forms; measure hyperbolicity; minimal models S. Lang, ``Hyperbolic and Diophantine analysis'', Bull. Amer. Math. Soc. (N.S.)14 (1986) no. 2, p. 159-205
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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. \(k\)-jet ampleness; blow-ups; \(k\)-th order embeddings; minimal degree projective varieties; complete intersection; determinantal varieties M.C. Beltrametti and A.J. Sommese, ''Notes on embeddings of blowups'', to appear in J. of Algebra.
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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. elliptic curve; height function; number of torsion points
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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. archimedean absolute values; Eisenstein constant; construction of bases; Riemann-Roch space; divisor; function field of a plane curve; height; degree; non-archimedean absolute values; Puiseux series Schmidt, W.M.: Construction and estimation of bases in function fields. J. Number Theory 39, 181--224 (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. intersection of surfaces; pencils of quadrics; curve parameterization; singular intersections Dupont, L., Lazard, D., Lazard, S., Petitjean, S.: Near-optimal parameterization of the intersection of quadrics: III. Parameterizing singular intersections. J. Symb. Comput. 43(3), 216--232 (2008)
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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. Kakeya problem; constructible set; Bezout's theorem; intersection multiplicity; flexy surface; funny curve; projective cone; Fano variety Slavov, K.: Variants of the Kakeya problem over an algebraically closed field. Arch. math. 103, No. 3, 267-277 (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. torsion group of elliptic curve; torsion prime numbers D. Abramovich , Formal finiteness and the torsion conjecture on elliptic curves. A footnote to a paper: ''Rational torsion of prime order in elliptic curves over number fields'' by S. Kamienny and B. Mazur. Astérisque 228 (1995), Columbia University Number Theory Seminar ( New- York , 1992 ), 5 - 17 . MR 1330925 | Zbl 0846.14013
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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-valued mapping; KKM mapping; topological vector space; quasi-equilibrium problem; intersection theorem
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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 curve; 4-manifold; Riemann surface; algebraic actions of a product of cyclic groups on simply-connected algebraic surfaces; actions which are non-trivial on homology; fixed point sets; automorphisms of the intersection form
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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. Poincaré series; complete intersection; differentials of quasihomogeneous singularities; local cohomology; Hodge structure Aleksandrov, A.G.: Cohomology of a quasi-homogeneous complete intersection. Math. USSR Izv.26 (1986), 437--477
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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. Bezout's theorem for the intersection of two projective algebraic; varieties; complete intersection; intersection numbers; g-multiplicity system; improper intersections; Bezout's theorem for the intersection of two projective algebraic varieties D. Kirby, ''On Bezout's theorem,''Quart. J. Math.,39, No. 156, 468--481 (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. defining equations; elliptic curve; 3-dimensional Sklyanin algebra; quadratic algebra; twisted homogeneous coordinate ring; elements of degree \(p\); cyclicity Le Bruyn, L.: The arithmetic of Sklyanin algebras I: the defining equations,Comm. Algebra (to appear).
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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. vertex set; space curve; geometry of surfaces; umbilic point; bifurcation diagram; family of curves; Euclidean invariant
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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. \(\mu\)-basis; elimination; matrix-based representations; intersection problems; singularities of algebraic curves; algebraic rational curve; projective space; computer aided geometric design Busé, L.; Thang, L. B., Matrix-based implicit representations of rational algebraic curves and applications, Comput. Aided Geom. Des., 27, 9, 681-699, (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. Buchsbaum module; regularity of homogeneous polynomial ideals; radical ideal DOI: 10.1007/BF02568752
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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. height of a Heegner point; \(L\)-series of the elliptic curve; conjecture of Birch and Swinnerton-Dyer Gross, B. H., Kolyvagin\(###\)s work on modular elliptic curves, (Coates, J.; Taylor, M. J., \textit{L}-Functions and Arithmetic, (1991), Cambridge University Press), 235-256
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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. modular curve; intersection of a modular symbol; intersection pairing Merel L., Manuscripta Math. 80 pp 283-- (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. complete intersection of a smooth cubic hypersurface and a quadratic hypersurface; Fano 3-fold; rationality A. Alzati - M. Bertolini , On the problem of rationality for some cubic complexes , Indag. Mat. , 91 ( 1988 ), pp. 349 - 364 . MR 976520 | Zbl 0683.14015
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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. Fermat curve; isogeny of Jacobians; minimal regular models; Néron models
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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. supersingular curve; complete Edwards curve; twisted Edwards curve; quadratic Edwards curve; twisted pair; order of point; Legendre's symbol; quadratic residue; quadratic nonresidue
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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; ideal; family of ideals; sandwich technique
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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. border basis; ideal of points; quasi border basis; vanishing ideal; buchberger-Möller algorithm
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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. height; intersection of projective varieties; normalized height; abelian variety; Néron-Tate height; torsion points Philippon, P.; Sur des hauteurs alternatives. III; J. Math. Pures Appl.: 1995; Volume 74 ,345-365.
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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 scheme; generic set of points in projective space; minimal graded free resolution; minimal resolution conjecture Hirschowitz, A.; Simpson, C., La résolution minimale de l'idéal d'un arrangement général d'un grand nombre de points dans \(\mathbb{P}^n\), Invent. Math., 126, 3, 467-503, (1996)
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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 reduction of ideal; Noetherian local ring Corso A. and Polini C. (1997). Reduction number of links of irreducible varieties. J. Pure Appl. Algebra 121: 29--43
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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. projective curve; defining ideal of a 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. effective test for the membership problem in the case of a polynomial complete intersection Dickenstein, A.; Sessa, C., An effective residual criterion for the membership problem in \textit{C}[z1,...,zn], J. pure appl. algebra, 74, 149-158, (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. isoptic curve; orthoptic curve; equioptic curve; spiric curve; quasi-equioptic; orthoptic point; equioptic point of three curves Odehnal, B.: Equioptic curves of conic sections. J. Geom. Graph. 14(1), 29-43 (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. action of subgroups of general linear group; invariant space as; complete intersection Nakajima, H.; Watanabe, K.: The classification of quotient singularities which are complete intersections. Lecture notes in math. 1092 (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. variety dominated by images of a curve; Mori's program; smooth quasi-projective variety; log del Pezzo surfaces Keel, Seán; McKernan, James, Rational curves on quasi-projective surfaces, Mem. Amer. Math. Soc., 140, 669, viii+153 pp., (1999)
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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; curve singularity; Tjurina number; Milnor number; delta invariant; normalization Dimca, A.; Greuel, G.-M., On 1-forms on isolated complete intersection curve 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. Hilbert scheme; locally complete intersection curve; hyperplane section
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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. Tate conjecture; Hodge conjecture; Beilinson-Bloch-Deligne conjectures; special values of L-functions; Shimura varieties; Baily-Borel-Satake compactification; motivic decomposition; intersection cohomology; non-CM abelian varieties; evaluation of height pairings
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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. Mordell-Weil lattice; elliptic curve over function field of rank 8; rational points generating the Mordell-Weil group
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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 structure; minimal rational curve; variety of minimal rational tangents; tangent map; analytic continuation; Cauchy characteristic; curvature; prolongation; parallel transport; nef tangent bundle; distribution; differential system; deformation rigidity Mok, Ngaiming, Geometric structures on uniruled projective manifolds defined by their varieties of minimal rational tangents, Astérisque, 322, 151-205, (2008)
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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; Hartshorne-Rao module; system of generators; resolution; Kronecker's embedding theorem; liaison theorems for quasi-complete intersections; arithmetically Buchsbaum projective schemes; k-Buchsbaum curves M. Fiorentini and A.T. Lascu, Projective embeddings and linkage. Rend. Sem. Mat. Fis. Milano57, 161--182 (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. linearly normal curve; power of the ideal sheaf; Castelnuovo-Mumford's regularity; non-special embedding Vermeire, P, Regularity and normality of the secant variety to a projective curve, J. Algebra, 319, 1264-1270, (2008)
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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. height of vector bundle; fundamental group scheme; smooth projective curve over a \(p\)-adic field; arithmetic surface C. Gasbarri, Heights of Vector Bundles and the Fundamental Group Scheme of a Curve. Duke Math. J. 117 No.2 (2003), 287-311. Zbl1026.11057 MR1971295
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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. Hilbert series of a graded algebra; complete intersection Fröberg, R.; Löfwall, C., On Hilbert series for commutative and noncommutative graded algebras, J. Pure Appl. Algebra, 76, 33-38, (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. deformation; Gorenstein local ring; linkage class; licci ideals; complete intersection; smoothable in codimension 3; embedding codimension; completion \beginbarticle \bauthor\binitsC. \bsnmHuneke and \bauthor\binitsB. \bsnmUlrich, \batitleLocal properties of licci ideals, \bjtitleMath. Z. \bvolume211 (\byear1992), page 129-\blpage154. \endbarticle \OrigBibText C. Huneke and B. Ulrich, Local properties of licci ideals, Math. Z. 211 (1992), 129-154. \endOrigBibText \bptokstructpyb \endbibitem
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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. invariants of reductive algebraic groups; normalization of separating subalgebras; inseparable closure; algorithm for generating set; MAGMA Kemper G.: Computing invariants of reductive groups in positive characteristic. Transform. Groups 8, 159--176 (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. analytic cycles; Nullstellensatz; quasi-complete intersection; isolated intersection Cygan, E.: Nullstellensatz and cycles of zeroes of holomorphic mappings, Ann. polon. Math. 78, 181-191 (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. Arakelov theory; genus 3 curves; modular height; self-intersection of the dualizing sheaf
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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. tangent line; trisecant line; quadric hypersurface; complete intersection of quadrics
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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. normal reduction number; normal surface singularity; geometric genus; elliptic singularity; Brieskorn complete intersection; homogeneous hypersurface singularity
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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. quotients by complex conjugation; real complete intersection surfaces; connected sums; products of real spheres; \(CDQ\)-surfaces; topological types S. Finashin, Decomposability of quotients by complex conjugation for complete intersection surfaces, Rev. Mat. Univ. Complut. Madrid, to appear.
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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. Castelnuovo-Mumford regularity; complete intersection; degree of projective schemes; Hilbert function; regularities Chardin, M., Philippon, P.: Régularité et interpolation. J. Algebr. Geom. \textbf{8}, 471-481 (1999). Erratum in J. Algebr. Geom. \textbf{11}, 599-600 (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. positive characteristic; complete intersection; not hyperplanar equimultiple curve; equimultiple locus Narasimhan R.: Monomial equimultiple curves in positive characteristic. Proc. Am. Math. Soc. 89, 402--413 (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. subcanonical curves; unstable bundles; space curve; complete intersection [C-V]1 Chiantini L., Valabrega P.,On some properties of subcanonical curves and unstable bundles. Comm. in Algebra (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. tangent cone; minimal set of generators; standard base; Koszul complex ROBBIANO, L. and VALLA, G.: Free resolutions of special tangent cones.Commutative Algebra.Proceedings of the Trento Conference.Lect.Notes in Pure and Appl. Math.Series,84.Marcel Dekker(l983)
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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. multiplicity of intersection; factorization theorem for the polar of an algebroid curve Ancochea Quevedo, G.: Curvas algebraicas sobre cuerpos cerrados de característica cualquiera. Memorias de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid. Serie de Ciencias exactas. Tomo IV. Memoria n. 1
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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. almost complete intersection; algebraic linkage; residual intersection; system of generators; regular sequences; ideals of the weak principal class
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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. Bézout theorem; height; logarithmic height of a generic point; geometric degree; height of the proper intersection of two subvarieties Jean-Benoît Bost, Henri Gillet, and Christophe Soulé, Un analogue arithmétique du théorème de Bézout, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 11, 845 -- 848 (French, with English summary).
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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. tight double linkage; rigid algebra; Gorenstein ideal; almost complete intersection DOI: 10.1016/0021-8693(85)90110-3
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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. graded Betti number; arithmetically Cohen-Macaulay scheme; partial intersection subscheme; Hilbert function; generators of the vanishing ideal; syzygies Ragusa, A.; Zappalà, G.: Partial intersection and graded Betti numbers. Beitr. algebra geom. 44, No. 1, 285-302 (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. finitely generated modules; free resolutions; cohomology of a complex of locally free sheaves; cohomology of a four-term complexes; locally free sheaves; normal toric varieties; derived categories; consistent dimer model algebras; Cox ring; Cox irrelevant ideal; finitely generated modules; free resolutions; cohomology of a complex of locally free sheaves; cohomology of a four-term complexes; locally free sheaves; normal toric varieties; Macaulay2, circuits in complete graphs A. Craw and A. Quintero Vélez, Cohomology of wheels on toric varieties, Hokkaido Math. J., to appear.
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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. Nagata P-ring; local flat homomorphism of local rings; P-homomorphism; complete intersection property; Cohen-Macaulay DOI: 10.1016/0021-8693(84)90164-9
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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. a-subcanonical smooth curve; 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. semifactorial hypersurfaces; cubic hypersurfaces; divisor; classification; complete intersection; variety of the chords of the Veronese surface
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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. smooth curve on a smooth complete intersection surface; normal bundles; Veronese surface K. Hulek : Complete intersection curve, the splitting of the normal bundle and the Veronese surface . Preprint Erlangen.
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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 projective variety of dimension \(2m+1\); cylinder homomorphism; Abel-Jacobi map; very ample line bundles; vanishing cycles; complete intersection of odd dimension
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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; monomial ideal; normal ideal; integral closure of graded rings; Serre condition K. Altmann, N. O. Ilten, L. Petersen, H. Süss, R. Volmert, \textit{The geometry of T-varieties}, in: \textit{Contributions to Algebraic Geometry}, EMS Ser. Congr. Rep., Eur. Math. Soc., Zu''rich, 2012, pp. 17-69.
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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. Rational points; Seminar; Bonn; Wuppertal; Mordell conjecture; proof of Tate conjecture; proof of Shafarevich conjecture; proof of the Mordell conjecture; logarithmic singularities; compactification of the moduli space of abelian varieties; modular height of an abelian variety; p-divisible groups; intersection theory on arithmetic surfaces; Riemann-Roch theorem; Hodge index theorem G. Faltings , G. Wüstholz , Rational Points, Aspects of Mathematics No. E6 , Vieweg, Braunschweig/Wiesbaden, 1984.
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