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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) cone; normal Cohen-Macaulay variety; non-rational singularities; 3- dimensional Gorenstein varieties Beltrametti, M., Sommese, A.: A criterion for a variety to be a cone. Comm. Math. Helv.62, 417-422 (1987)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) points in multiprojective spaces; arithmetically Cohen-Macaulay; linkage
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) flag varieties; Schubert polynomials; Grothendieck polynomials; simplicial complexes
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) local cohomology; arithmetically Cohen-Macaulay curves; Buchsbaum; tetrahedral curves; deficiency module; Fourier-Motzkin Giang, DH; Hoa, LT, On local cohomology of a tetrahedral curve, Acta Math. Vietnam, 35, 229-241, (2010)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) \(p\)-Sylow subgroups; Cohen-Macaulay ring; Buchsbaum ring; modular rings of invariants; shallow representation Campbell H.E.A., Hughes I.P., Kemper G., Shank R.J., Wehlau D.L.: Depth of modular invariant rings. Transform. Groups 5(1), 21--34 (2000)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Dynkin quivers; orbit closures; Cohen-Macaulay varieties; rational singularities; path algebras; translation quivers Bobiński, Grzegorz; Zwara, Grzegorz, Normality of orbit closures for Dynkin quivers of type \(\mathbb{A}_n\), Manuscripta Math., 105, 1, 103-109, (2001)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) projective curve; hyperplane section; arithmetically Cohen-Macaulay curve; arithmetically Gorenstein curve
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) quadric; Bernstein-Gelfand-Gelfand correspondence; maximal Cohen- Macaulay; Clifford algebra; linear module; MCM modules Buchweitz, Ragnar-Olaf; Eisenbud, David; Herzog, Jürgen, Cohen-Macaulay modules on quadrics, (), 58-116
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) arithmetically Cohen-Macaulay sheaf; representation type; surface
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) coordinate ring of quantum matrices; coordinate ring of quantum \(n \times n\) matrices; automorphisms; defining relations; variety; point modules; graded flat deformations; polynomial rings; homogeneous Poisson brackets; Poisson structures; symplectic leaves Vancliff, M.: The defining relations of quantum n\(\times n\) matrices. J. lond. Math. soc. (2) 52, No. 2, 255-262 (1995)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay variety; defining equations; ideal sheaf; codimension 2 Paolo Maroscia and Wolfgang Vogel, On the defining equations of points in general position in \?\(^{n}\), Math. Ann. 269 (1984), no. 2, 183 -- 189.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) star configuration; scheme; minimal free resolution
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) minimal free resolution; complexity; Gorenstein ring; cohomology; local complete intersection ring; Gorensteinness ______, \emph{Support varieties and cohomology over complete intersections}, Invent. Math. \textbf{142} (2000), no.~2, 285--318. \MR{1794064 (2001j:13017)}
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) deformation of manifold and coherent sheaf; differential graded algebra; locally free resolution;trace morphism; hypercohomology; determinant bundle; tangent space; obstruction space; deformation problem controlled; simplicially enriched model category of DG-Lie algebras; module of derivations of pairs; differential operators with principal symbol
0
Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) multi-homogeneous coordinate ring; invertible bimodule; Rees algebra; projective scheme; ascending chain condition; non-commutative algebraic geometry; quasi-coherent sheaves; graded modules modulo torsion submodules; homogeneous coordinate rings Chan, D.: Twisted multi-homogeneous coordinate rings. J. algebra 223, 438-456 (2000)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Hilbert function; minimal free resolution of the homogeneous ideal of a \(k\)-configuration A. V. Geramita and Y. S. Shin, \(k\)-configurations in \(\mathbb{P}^3\) all have extremal resolutions, J. Algebra 213 (1999), 351--368.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) local Noetherian ring; ideal; height; minimum number of generators; complete intersection; conormal module; analytic spread; projective dimension; canonical module; Cohen-Macaulay ideals; Gorenstein ideals DOI: 10.1016/0022-4049(85)90023-4
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) type vector; finite set of points in \(\mathbb{P}^n\); Hilbert functions; \(k\)-configurations; arrangements; number of minimal generators; lex-segment ideal; maximal graded Betti numbers; liaison Geramita, A. V.; Harima, T.; Shin, Y. S.: Extremal point sets and Gorenstein ideals. Queen's papers in pure and appl. Math. 114, 99-140 (1998)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Hilbert-Samuel polynomials; generalized Cohen-Macaulay module; standard system of parameters; standard s.o.p.; local cohomology; M-sequences; d- sequences; form module; Rees module Trung N.V.: Toward a theory of generalized Cohen--Macaulay modules. Nagoya Math. J. 102, 1--49 (1986)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay property; multi-Rees algebra; analytic spread; Cohen-Macaulayness Hyry, E., Cohen-Macaulay multi-Rees algebras, Compos. Math., 130, 319-343, (2002)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) noncommutative resolutions; CM modules; surface singularities
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) scroll; representation type; Ulrich bundles; arithmetic Cohen-Macaulay sheaves Miró-Roig, R.M.: The representation type of rational normal scrolls. Rendiconti del Circolo Matematico di Palermo 62, 153-164 (2013)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) strongly \(k\)-normal curve; arithmetically Cohen-Macaulay surfaces; \(K3\) surfaces
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Buchsbaum-Eisenbud criterion; prime ideal of the monomial curve; minimal finite free resolution H. Bresinsky, Minimal free resolutions of monomial curves in \(\mathbb{P}\) k 3 . Linear Alg. Appl.59, 121--129 (1984)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Bridgeland stability conditions; derived categories; moduli spaces of sheaves and complexes; wall crossing; symplectic resolutions Meachan, C; Zhang, Z, Birational geometry of singular moduli spaces of O'grady type, Adv. Math., 296, 210-267, (2016)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) degrees of smooth threefolds; not arithmetically Cohen-Macaulay; liaison Rosa M. Miró-Roig, The degree of smooth non-arithmetically Cohen-Macaulay threefolds in \?\(^{5}\), Proc. Amer. Math. Soc. 110 (1990), no. 2, 311 -- 313.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) ADE singularities; hypersurface singularities of finite deformation type; hypersurface singularities with finite Cohen-Macaulay type; normal forms for simple singularities Greuel, G.-M., Kröning, H.: Simple singularities in positive characteristic. Math. Z. 203(2), 339-354 (1990). Zbl 0715.14001
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Ulrich bundles; del Pezzo surfaces; arithmetically Cohen-Macaulay vector bundles Casnati, G.: Rank two aCM bundles on general determinantal quartic surfaces in \({\mathbb{P}}^3\). Ann. Uni. Ferrara (2016). 10.1007/s11565-016-0244-0
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) stable category; Cohen-Macaulay module; noncommutative quadric hypersurface; adjacency matrix; Stanley-Reisner ideal
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) depth of a module; resolutions of Jacobi modules; non-isolated hypersurface singularities; unfoldings; deformations; Jacobi ideal; projective dimension Pellikaan, G. R.: Hypersurfaces singularities and resolutions of Jacobi modules. (1985)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay; \(n\)-cluster tilting; \(K\)-theory; hypersurface singularities; automorphism groups
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) K-theory; 1-dimensional Cohen-Macaulay scheme Weibel, C.: K-theory of 1-dimensional schemes. AMS contemp. Math. 55, 811-818 (1986)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) de Rham complexes; free divisors; hyperplane arrangements; logarithmic vector fields; Bernstein polynomial Torrelli, T.: Logarithmic comparison theorem and \({\mathcal{D}}\) -modules: an overview. In: Denis Chéniot et al. (ed.) Singularity Theory: Dedicated to Jean--Paul Brasselet on His 60th Birthday, pp. 996--1010. World Scientific, New York (2007)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) bilinear pairing map; free modules; elliptic curves; cryptography Lee, H. -S.: A self-pairing map and its applications to cryptography. Appl. math. Comp. 151, No. 3, 671-678 (2004)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) general linear groups; irreducible representations; minimal resolutions; Betti tables; Boij-Söderberg theory; symmetric functions; Schur functors; pure resolutions; equivariant resolutions; Betti diagrams; determinantal varieties Sam, S. V; Weyman, J., \textit{Pieri resolutions for classical groups}, J. Algebra, 329, 222-259, (2011)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) algebra; modules; fields; complexes; groups; commutative algebra; homological algebra; algebraic geometry; function theory; number theory S. Lang, \textit{Algebra} (Springer, New York, 2002).
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) homotopy algebras; Gerstenhaber algebras; graded vector spaces; Poisson algebras; little disks operad; Hochschild cohomology; geometry of configurations of points; Hochschild complexes A. A. Voronov, Homotopy Gerstenhaber algebras, Conférence Moshé Flato 1999: Quantization, Deformation, and Symmetries. Vol. II (Dijon 1999), Math. Phys. Stud. 22, Kluwer Academic Publishers, Dordrecht (2000), 307-331.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) formal neighborhoods; derived categories; differential graded algebras; differential graded categories; cohesive modules Yu, S.: Dolbeault dga of a formal neighborhood. Trans. amer. Math. soc. 368, No. 11, 7809-7843 (2016)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) transversality; arithmetically Cohen-Macaulay curves
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) geometric genus; quasihomogeneous isolated singularity; minimal resolutions
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) \(\mathbb{Q}\)-factorial complete toric varieties; Cartier and Weil divisors; pure modules; free and torsion subgroups; localization; completion of fans
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) rational curves; Riemann-Roch theorem; liaison; arithmetical Cohen-Macaulay; linkage Daniel Perrin, Géométrie algébrique, Savoirs Actuels. [Current Scholarship], InterEditions, Paris; CNRS Éditions, Paris, 1995 (French, with French summary). Une introduction. [An introduction].
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) fat points; infinitesimal neighborhood; Hilbert function; minimal free resolution; double points; Horace lemma; residue; defect
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay; \(D+M\) construction; embedding dimension; Gorenstein; idealization; Krull dimension; pullback; Zariski topology
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) geometrically regular \(k\)-algebra; homologies of complexes; cyclic homology; filtration; De Rham homologies; differential modules Group, Buenos Aires Cyclic Homology: Hochschild and cyclic homology of hypersurfaces, Adv. math. 95, No. 1, 18-60 (1992)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) algebraic curve; Green's conjecture; anticanonical surface; minimal free resolution Lelli-Chiesa, Margherita, Green's conjecture for curves on rational surfaces with an anticanonical pencil, Math. Z., 275, 3-4, 899-910, (2013)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) regular algebras; quadratic algebras; projective geometry; quadrics; commutation relations; graded Clifford algebras; two-parameter deformations; defining relations; point modules; iterated Ore extensions; line modules Vancliff, M.; Van Rompay, K.; Willaert, L., Some quantum \({\mathbf P}^3\)s with finitely many points, Comm. Algebra, 26, 4, 1193-1208, (1998)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Gorenstein liaison; complete intersection liaison; G-linkage; G-liaison; arithmetically Cohen-Macaulay schemes; unobstructedness; Hilbert flag schemes Kleppe, J.; Migliore, J.; Miró-Roig, R. M.; Nagel, U.; Peterson, C., Gorenstein liaison, complete intersection liaison invariants and unobstructedness, Mem. Am. Math. Soc., 154, 732, (2001)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) gonality conjecture; Green-Lazarfeld conjecture; toric surfaces; syzygy; minimal free resolution Kawaguchi, R.: The gonality conjecture for curves on toric surfaces with two \(\mathbb{P}\)1-fibrations. Saitama Math. J. 27, 35--80 (2010)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) topological Hochschild homology; cyclotomic spectra; Cartier modules; Dieudonné modules; de Rham-Witt complexes
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) graded rings; Artin-Schelter regular algebras of global dimension three; noncommutative projective geometry; elliptic algebras; point modules; Noetherian domains; Hilbert series; elliptic curves -, Algebras associated to elliptic curves , Trans. Amer. Math. Soc. 349 (1997), 2317--2340. JSTOR:
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) pg-ideal; Rees algebra; normal Hilbert coefficient; Cohen-Macaulay; rational singularity T. Okuma, K.-I. Watanabe and K.-I. Yoshida, Rees algebras and \(p_g\)-ideals in a two-dimensional normal local domain, Proc. Amer. Math. Soc. 145 (2017), no. 1, 39--47.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) generic matrix; determinantal ideals; Cohen-Macaulay normal domain; divisor class group; symmetric algebra W. Bruns andA. Simis, Symmetric algebras of modules arising from a fixed submatrix of ageneric matrix. J. Pure. Appl. Algebra49, 227-245 (1987).
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) McMullen's upper bound theorem; Cohen-Macaulay complex; survey; torus action; simple convex n-polytope M.\ W. Davis and T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991), no. 2, 417-451.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) holonomic module; V-filtration; duality; Cohen-Macaulay; vanishing cycle functors M. Saito, Duality for vanishing cycle functors, Publ. RIMS 25 (1989), 889--921. DOI: 10.2977/prims/1195172510
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) glicci; Picard group; Gorenstein liaison; arithmetically Cohen-Macaulay subscheme; Gorenstein-linked to a complete intersection M. Casanellas andR.M. Miró-Roig,Gorenstein liaison of curves in \(\mathbb{P}\) 4, J. Alg.230 (2000), 656--664.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) o-minimal; equivariant Morse theory; definable \(C^{2}\) groups; equivariant definable Morse functions; critical points; critical values; open definable \(G CW\) complexes
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) arithmetically Cohen-Macaulay; monads; quadrics; spinors DOI: 10.1007/s10231-008-0084-3
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay map; flat family; local duality; quotient category; base change Ile, R., Cohen-Macaulay approximation in fibred categories, J. Algebra, 367, 142-165, (2012), MR 2948215
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) arithmetically Cohen-Macaulay vector bundles; cubic fourfolds Lahoz, M.; Macrì, E.; Stellari, P., Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane, (Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic, Prog. Math., vol. 320, (2017), Birkhäuser/Springer), 155-175
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Kac-Moody Lie algebra; Schubert variety; normal Cohen-Macaulay variety; Weyl-Kac character formula S. Kumar, ''Demazure character formula in arbitrary Kac-Moody setting,'' Invent. Math., vol. 89, iss. 2, pp. 395-423, 1987.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Determinantal hypersurfaces; arithmetically Cohen-Macaulay sheaves; kernel sheaves; multiple hypersurfaces; sheaves on multiple hypersurfaces; hyperbolic polynomials Kerner, D.; Vinnikov, V., Determinantal representations of singular hypersurfaces in \(\mathbb{P}^n\), Adv. Math., 231, 1619-1654, (2012)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) generalized extremal algebras; Artin-Schelter regular algebras; Hilbert series; Auslander regular algebras; Cohen-Macaulay algebras; Calabi-Yau algebras
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) connected complex semisimple Lie groups; Lie algebras; maximal compact subgroups; flag variety; irreducible Harish-Chandra modules; global sections; irreducible \(\mathcal D\)-modules; minimal \(K\)-types
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) ramified covering maps; covering maps; simplicial sets; simplicial complexes Aguilar, M.; Prieto, C.: Simplicial ramified covering maps, Topology appl. 156, 205-216 (2008)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) graded connected algebras; Castelnuovo-Mumford regularity; balanced dualizing complexes Dong, Z.-C.; Wu, Q.-S., Non-commutative Castelnuovo-Mumford regularity and AS-regular algebras, J. Algebra, 322, 1, 122-136, (2009)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) local cohomology; Serre duality; dualizing complexes; graded rings; Grothendieck duality; coherent sheaves; Matlis duality; filtered rings; filtrations; Gorenstein rings van den Bergh, M., Existence theorems for dualizing complexes over non-commutative graded and filtered rings, \textit{J. Algebra}, 195, 2, 662-679, (1997)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Division algebra; unit group; building; vector bundle; modification; Chern class; locally free sheaves of modules over Azumaya algebras: DOI: 10.1007/978-3-0346-0288-4_7
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) openness of loci; Cohen-Macaulay property; Gorenstein property; effective computability; Fitting invariants; complete intersection F. Rossi and W. Spangher, Some effective methods in the openness of loci for Cohen-Macaulay and Gorenstein properties, inEffective Methods in Algebraic Geometry, Proc. Intern. Conf. MEGA 90, Castiglioncello 1990, T. Mora and C. Traverso, eds., Progress in Mathematics94, Birkhäuser (1990), 441-455.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) determinantal variety; minimal free resolution P. Pracacz and J. Weyman, Complexes associated with trace and evaluation: Another approach to Lascoux's resolution, Adv. Math. 57 (1985), 163--207.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) determinantal ideal; minimal free resolution
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) arithmetically Cohen-Macaulay; vector bundle; cubic threefold; quartic threefold Biswas I., Biswas J., Ravindra G.V.: On some moduli spaces of stable vector bundles on cubic and quartic threefolds. J. Pure Appl. Algebra 212(10), 2298--2306 (2008)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) minimal free resolution; Betti number; rational normal scroll; varieties of low degree; \texttt{Singular} Lee, Classification of Betti diagrams of varieties of almost minimal degree, J. Korean Math. Soc. 48 (5) pp 1001-- (2011)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) syzygy; minimal free resolution; canonical curve
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) syzygies; Hirzebruch surfaces; free resolutions
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) \(F\)-rational ring; prime characteristic; tight closure; balanced big Cohen-Macaulay module; pseudo-rational singularities K. E. Smith, ''Tight closure of parameter ideals,'' Invent. Math., vol. 115, iss. 1, pp. 41-60, 1994.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) degeneration; Gröbner bases; simplicial complexes; Stanley-Reisner schemes; matrix Schubert varieties; ladder determinantal ideals; diagonal term orders A. Knutson, E. Miller, and A. Yong, \textit{Gröbner geometry of vertex decompositions and of flagged tableaux}, J. Reine Angew. Math., 630 (2009), pp. 1--31.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) residue complexes; three-dimensional Sklyanin algebras; quantum polynomial rings; multiplicites; point modules; quantum anomalies Ajitabh, K.: Residue complex for Sklyanin algebras of dimension three. Adv. math. 144, 137-160 (1999)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Hochschild cohomology; smooth separated schemes; relative tangent sheaves; cohomology sheaves; continuous Hochschild cochains; injective resolutions; Hochschild complexes; derived categories Yekutieli A.: The continuous Hochschild cochain complex of a scheme. Can. J. Math. 54(6), 1319--1337 (2002)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) quantum flag manifolds; straightening laws; Cohen-Macaulay; Gorenstein S. Kolb, The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weight. J. Algebra 319 (2008), 3518-3534.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) minimal resolution; fat points; Hilbert function; graded Betti numbers G. Fatabbi, Ideals of fat points and splittable ideals, inThe Curves Seminar at Queen's, Vol. 10, Queen's Papers in Pure and Applied Mathematics, Vol. 102, pp. 242--255.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) surfaces; Ulrich bundles; arithmetically Cohen-Macaulay; geometric genus; irregularity
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) arithmetically Cohen Macaulay bundles; complete intersections; normal function Biswas, J.; Ravindra, G. V., Arithmetically Cohen-Macaulay bundles on complete intersection varieties of sufficiently high multi-degree, Math. Z., 265, 3, 493-509, (2010)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Macaulayfication; dualizing complex; \(p\)-standard system of parameters; \(d\)-sequence; Sharp's conjecture; blowing-up; Cohen-Macaulay scheme; desingularization; Noetherian scheme T. Kawasaki, ''On Macaulayfication of Noetherian schemes,'' Trans. Amer. Math. Soc., 352, No. 6, 2517--2552 (2000).
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cremona transformations; syzygy matrix; arithmetically Cohen-Macaulay base locus K. Hulek, S. Katz, and F.O. Schreyer, Cremona transformations and syzygies,Math. Z. 209 (1992), 419--443.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Cohen-Macaulay; excellence; Macaulayfication; resolution of singularities
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) noncommutative geometry; quantum toric varieties; semigroup algebras; Artin-Schelter; Cohen-Macaulay; Artin-Schelter Gorenstein Rigal, L.; Zadunaisky, P., Twisted semigroup algebras, \textit{Alg. Rep. Theory}, 5, 1155-1186, (2015)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) extremal rays; minimal model program; MMP; terminal singularities; Picard numbers; directed flip; graded canonical ring; threefold; Kodaira dimension; divisorial contractions Mori, Shigefumi. \(Flip theorem and the existence of minimal models for 3-folds\). J. Amer. Math. Soc. 1 (1988), no. 1, 117-253.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) two planes crossing at a point; not Cohen-Macaulay Zwara, G, An orbit closure for a representation of the Kronecker quiver with bad singularities, Colloq. Math., 97, 81-86, (2003)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Gerko Cohen-Macaulay dimension; Gorenstein dimension; semi-dualizing module; Cohen-factorization; Auslander-Buchsbaum equality
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Saito's divisor; subspace of singularities; Cohen-Macaulay space; local duality; isolated singularities Aleksandrov, AG, Nonisolated Saito singularities, Math. USSR Sbornik, 65, 561-574, (1990)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) triangle singularity; matrix factorization; weighted projective line; vector bundle; singularity category; Cohen-Macaulay module; projective cover; injective hull
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) orbits; adjoint actions; Zariski closures; Cohen-Macaulay variety; rational singularities Donkin S., ''The normality of closures of conjugacy classes of matrices,'' Invent. Math., 101, No. 3, 717--736 (1990).
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) Ulrich sheaves; arithmetically Cohen-Macaulay
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) graded rings of Siegel modular forms; theta constants; coding theory; Specht modules; Igusa desingularization; Humbert surfaces; hyperelliptic points Runge B.: Level-Two-Structures and Hyperelliptic Curves. Osaka J. Math. 34, 21--51 (1997)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) maximal Cohen-Macaulay module; finite Cohen-Macaulay representation type; isolated singularity; hypersurface ring; Auslander-Reiten sequences; Auslander-Reiten quiver; MCM approximations Leuschke G.\ J. and Wiegand R., Cohen-Macaulay representations, Math. Surveys Monogr. 181, American Mathematical Society, Providence 2012.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) algebro-geometric cohomology theories; intersection cohomology; perverse sheaves; representations of Lie algebras; sheaves; flag varieties; simplicial complexes M. Vybornov, Perverse sheaves, Koszul IC-modules, and the quiver for the category O, preprint arXiv:math.AG/0309247.
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) deformation theory; obstruction; Hilbert scheme; locally Cohen-Macaulay curves; Gorenstein zero-dimensional scheme
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) determinantal rings; Cohen Macaulay ideal; initial algebra; Ulrich ideals; multiplicity Bruns, W.; Römer, T.; Wiebe, A., Initial algebras of determinantal rings, Cohen-Macaulay and ulrich ideals, \textit{Michigan Math. J.}, 53, 71-81, (2005)
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Cohen-Macaulay modules; graded minimal free resolutions; simplicial complexes; chessboard complexes; matching complexes Reiner V., Roberts J.: Minimal resolutions and the homology of matching and chessboard complexes. J. Algebraic Combin. 11(2), 135--154 (2000) coherent rings; graded algebras; noncommutative schemes; Gorenstein algebras; categories of coherent modules; coherent sheaves D. Piontkovski, Coherent algebras and noncommutative projective lines. J. Algebra 319 (2008), 3280-3290.
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