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O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Cohen-Macaulay modules, Plane and space curves
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Singularities of curves, local rings, Cohen-Macaulay modules, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Determinantal varieties, Linkage, complete intersections and determinantal ideals
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Toric varieties, Newton polyhedra, Okounkov bodies, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Lorenzini, A., Betti numbers of points in projective space, J. Pure Appl. Algebra, 63, 181, (1990) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Polynomial rings and ideals; rings of integer-valued polynomials, Structure, classification theorems for modules and ideals in commutative rings, Projective techniques in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Formal groups, \(p\)-divisible groups, Geometric invariant theory, Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Group actions on varieties or schemes (quotients), Formal power series rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Richard Fedder, \?-purity and rational singularity in graded complete intersection rings, Trans. Amer. Math. Soc. 301 (1987), no. 1, 47 -- 62. Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Polynomial rings and ideals; rings of integer-valued polynomials, Rational and unirational varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Billey, Sara; Lakshmibai, V., Singular loci of Schubert varieties, Progress in Mathematics, vol. 182, (2000), Birkhäuser Boston, Inc.: Birkhäuser Boston, Inc. Boston, MA, MR 1782635 Grassmannians, Schubert varieties, flag manifolds, Singularities in algebraic geometry, Research exposition (monographs, survey articles) pertaining to algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties N. Suwa, ''A note on Gersten's conjecture for logarithmic Hodge-Witt sheaves,'' \(K\)-Theory, vol. 9, iss. 3, pp. 245-271, 1995. \(p\)-adic cohomology, crystalline cohomology, Determinantal varieties, Finite ground fields in algebraic geometry, \(K\)-theory of schemes
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Barile, M.; Morales, M.; Thoma, A.: On systems of relations associated to toric semigroups. Queen's papers in pure and appl. Math. 123, 173-185 (2002) Toric varieties, Newton polyhedra, Okounkov bodies, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Complete intersections, Semigroup rings, multiplicative semigroups of rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Yanagawa, K.: On the regularities of arithmetically Buchsbaum curves. Math. Z. 226, 155-163 (1997) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Plane and space curves, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties DOI: 10.1080/00927878708823505 Special algebraic curves and curves of low genus, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Drozd, Yu.A., Cohen-Macaulay modules and vector bundles, (Proc. Euroconference in: Interactions Between Ring Theory and Representations of Algebras, Lect. Notes Pure Appl. Math., vol. 210, (2000), Marcel Dekker New York), 107-130 Cohen-Macaulay modules in associative algebras, Vector bundles on curves and their moduli, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Moduli, classification: analytic theory; relations with modular forms, Global theory and resolution of singularities (algebro-geometric aspects), Representation type (finite, tame, wild, etc.) of associative algebras, Cohen-Macaulay modules
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Beltrametti M.C., Sommese A.J.: On generically polarized Gorenstein surfaces of sectional genus two. J. Reine Angew. Math. 386, 172--186 (1988) Families, moduli, classification: algebraic theory, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Divisors, linear systems, invertible sheaves
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties M. Vybornov, ''Mixed algebras and quivers related to cell complexes,'' Comm. Algebra, vol. 25, iss. 12, pp. 3985-3992, 1997. Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc., Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Cellularity in topological manifolds
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties \(K3\) surfaces and Enriques surfaces, Curves in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Gorla, E.: The general hyperplane section of a curve, Trans. am. Math. soc. 358, No. 2, 819-869 (2006) Plane and space curves, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Polynomial rings and ideals; rings of integer-valued polynomials
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Surfaces of general type, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Rational and ruled surfaces
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties BELTRAMETTI M. C. and SOMMESE A. J., ''On k-jet ampleness, in Complex Analysis and geometry'', ed. by V. Ancona and A. Silva, (1993), Plenum Press, New York, 355--376. Divisors, linear systems, invertible sheaves, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Special surfaces
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Fisher, T.: Pfaffian presentations of elliptic normal curves, Trans. Amer. Math. Soc. \textbf{362} (2010), 2525--2540 Elliptic curves, Determinantal varieties, Syzygies, resolutions, complexes and commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Nagel, U., Lifting the \(k\)-Buchsbaum property, J. Pure Appl. Algebra, 152, 267-273, (2000) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Local cohomology and commutative rings, Local cohomology and algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Linkage, complete intersections and determinantal ideals, Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Rings with straightening laws, Hodge algebras, Secant varieties, tensor rank, varieties of sums of powers, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Kustin, A.; Miller, M.; Ulrich, B.: Linkage theory for algebras with pure resolutions. J. algebra 102, 199-228 (1986) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Complete intersections
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Commutative Noetherian rings and modules, Determinantal varieties, Multilinear algebra, tensor calculus, Representation theory for linear algebraic groups
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Beltrametti M. -Sommese A. J.,0-cycles and k-th order embeddings of smooth projective surfaces, Problems in the Theory of Surfaces, Proc. Cortona, 1988, to appear. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Families, moduli, classification: algebraic theory
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties G. Knese, ''Polynomials with no zeros on the bidisk,'' Anal. PDE, vol. 3, iss. 2, pp. 109-149, 2010. Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Linear operator methods in interpolation, moment and extension problems, Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.), Fourier series and coefficients in several variables, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Degtyarev, A.; Itenberg, I., On real determinantal quartics, (Proceedings of the Gökova geometry-topology conference 2010, (2011), Int. Press Somerville, MA), 110-128 Real algebraic and real-analytic geometry, Determinantal varieties, \(K3\) surfaces and Enriques surfaces
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Grzegorz Bobiński and Andrzej Skowroński, Geometry of directing modules over tame algebras, J. Algebra 215 (1999), no. 2, 603 -- 643. Representation type (finite, tame, wild, etc.) of associative algebras, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Linear algebraic groups over the reals, the complexes, the quaternions, Group actions on varieties or schemes (quotients), Complete intersections, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Finite rings and finite-dimensional associative algebras, Module categories in associative algebras
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Homogeneous spaces and generalizations, Birational geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Syzygies, resolutions, complexes and commutative rings, Determinantal varieties, Representations of quivers and partially ordered sets
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Kurano, K.: On relations on minors of generic symmetric matrices. J. algebra 124, 388-413 (1989) Geometric invariant theory, Determinantal varieties, Projective and free modules and ideals in commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties P. Bonacini, L. Marino, Hilbert functions and set of points in P1{\(\times\)} P1, Beiträge zur Algebra und Geometrie (DOI: 10.1007/s13366-014-0212-8, to appear).10.1007/s13366-014-0212-8, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Huneke C., Ulrich B.: General hyperplane sections of algebraic varieties. An introduction to a theorem of Strano. J. Algebr. Geom. 2, 487--505 (1993) Complete intersections, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Classical groups (algebro-geometric aspects), Determinantal varieties, Homogeneous spaces and generalizations, Toric varieties, Newton polyhedra, Okounkov bodies
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Miró-Roig, R. M.: On the theorem of Castelnuovo for Buchsbaum curves. Arch. math. (Basel) 52, 513-518 (1989) Special algebraic curves and curves of low genus, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Divisors, linear systems, invertible sheaves
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Vector bundles on curves and their moduli, Special divisors on curves (gonality, Brill-Noether theory), Determinantal varieties, Infinitesimal methods in algebraic geometry, Deformations and infinitesimal methods in commutative ring theory, Torelli problem
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Geramita, A. V., Harbourne, B., Migliore, J., Nagel, U.: Matroid configurations and symbolic powers of their ideals. Trans. Am. Math. Soc. (to appear) (2015). arXiv:1507.00380v1 Configurations and arrangements of linear subspaces, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Combinatorial aspects of matroids and geometric lattices, Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes, Combinatorial aspects of commutative algebra, Syzygies, resolutions, complexes and commutative rings, Linkage, complete intersections and determinantal ideals
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Fiorentini, M.; Vogel, W.: Old and new results and problems on Buchsbaum modules, I. Sem. geom. Univ. studi Bologna 1988--1991, 53-61 (1991) Cohen-Macaulay modules, Curves in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Commutative rings and modules of finite generation or presentation; number of generators, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Ellingsrud, Geir; Piene, Ragni; Strømme, Stein Arild, On the variety of nets of quadrics defining twisted cubics.Space curves, Rocca di Papa, 1985, Lecture Notes in Math. 1266, 84-96, (1987), Springer, Berlin Grassmannians, Schubert varieties, flag manifolds, Determinantal varieties, Pencils, nets, webs in algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Class groups, Linkage, complete intersections and determinantal ideals, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties S. Fitchett, Maps of linear systems on blow-ups of the projective plane, J. Pure Appl. Algebra, to appear. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Rational and ruled surfaces, Syzygies, resolutions, complexes and commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Glassbrenner, D.; Smith, K. E.: Sparse systems of parameters for determinantal varieties. Adv. in appl. Math. 19, 529-558 (1997) Determinantal varieties, Computational aspects of higher-dimensional varieties, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Jafari, R.; Zarzuela, S., On monomial curves obtained by gluing, \textit{Semigroup Forum}, 88, 2, 397-416, (2014) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Rosa M. Miró-Roig, Nonobstructedness of Gorenstein subschemes of codimension 3 in \?\(^{n}\), Beiträge Algebra Geom. 33 (1992), 131 -- 138. Parametrization (Chow and Hilbert schemes), Complete intersections, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Low codimension problems in algebraic geometry, Projective techniques in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Molinelli, S.; Patil, D. P.; Tamone, G.: On the Cohen--Macaulayness of the coordinate ring of certain projective monomial curves. Beiträge zur algebra und geometrie 40, 437-458 (1999) Cohen-Macaulay modules, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Polynomial rings and ideals; rings of integer-valued polynomials, Plane and space curves
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties [Tu] Tu, L.: Degeneracy loci. Proceedings, Berlin 1985, Teubner Verlag, Leipzig, 296--305 (1986) Topological properties in algebraic geometry, Structure of families (Picard-Lefschetz, monodromy, etc.), Classical real and complex (co)homology in algebraic geometry, Singularities in algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties W. Bruns, M. Varbaro, Young diagrams of single exterior type, in preparation. Actions of groups on commutative rings; invariant theory, Determinantal varieties, Group actions on varieties or schemes (quotients)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Complete intersections, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties D.C. Cohen, ''Triples of arrangements and local systems,'' Proc. Amer. Math. Soc. 130(10) (2002), 3025--3031. Relations with arrangements of hyperplanes, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Homology with local coefficients, equivariant cohomology, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties E. D. Davis, A. V. Geramita, and F. Orecchia, Hilbert functions of linked varieties, The curves seminar at Queen's, Vol. III (Kingston, Ont., 1983) Queen's Papers in Pure and Appl. Math., vol. 67, Queen's Univ., Kingston, ON, 1984, pp. Exp. No. F, 11. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Enumerative problems (combinatorial problems) in algebraic geometry, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Complete intersections, (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Representations of quivers and partially ordered sets, Determinantal varieties, Combinatorial aspects of groups and algebras, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, \(K\)-theory of schemes
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Mats Boij and Fabrizio Zanello, Level algebras with bad properties, Proc. Amer. Math. Soc. 135 (2007), no. 9, 2713-2722 (electronic). Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Commutative Artinian rings and modules, finite-dimensional algebras, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Integral dependence in commutative rings; going up, going down, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Extension theory of commutative rings, Ideals and multiplicative ideal theory in commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Determinantal varieties, Singularities of surfaces or higher-dimensional varieties, Global theory and resolution of singularities (algebro-geometric aspects), Local cohomology and commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Lauze F., Manuscripta Math 92 pp 525-- (1997) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Topological properties in algebraic geometry, Syzygies, resolutions, complexes and commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Matusevich, L.F., Miller, E., Walther, U.: Homological methods for hypergeometric families. J. Am. Math. Soc. 18(4), 919--941 (2005). arXiv:math.AG/0406383 Commutative rings of differential operators and their modules, Local cohomology and commutative rings, Other hypergeometric functions and integrals in several variables, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Kaji H. (2003). On the duals of Segre varieties. Geometriae Dedicata 99: 221--229 Projective techniques in algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Esnault, H.; Srinivas, V.; Viehweg, E., \textit{the universal regular quotient of the Chow group of points on projective varieties}, Invent. Math., 135, 595-664, (1999) Parametrization (Chow and Hilbert schemes), Abelian varieties and schemes, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Mireille Martin-Deschamps and Ragni Piene, Arithmetically Cohen-Macaulay curves in \?\(^{4}\) of degree 4 and genus 0, Manuscripta Math. 93 (1997), no. 3, 391 -- 408. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Plane and space curves, Arithmetic ground fields for curves, Cohen-Macaulay modules
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties BOLONDI,G.;Zeuthen problem and cohomology Preprint U.T.M.226, Trento (1987) Plane and space curves, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Projective techniques in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Sturmfels, B.; Zelevinsky, A., Maximal minors and their leading terms, \textit{Adv. Math.}, 98, 1, 65-112, (1993) Linkage, complete intersections and determinantal ideals, Polynomial rings and ideals; rings of integer-valued polynomials, Toric varieties, Newton polyhedra, Okounkov bodies, Determinantal varieties, Enumerative problems (combinatorial problems) in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Parallel algorithms in computer science, Software, source code, etc. for problems pertaining to algebraic geometry, Computational aspects in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Arnaud Beauville, Fibrés de rang deux sur une courbe, fibré déterminant et fonctions thêta. II, Bull. Soc. Math. France 119 (1991), no. 3, 259 -- 291 (French, with English summary). Theta functions and curves; Schottky problem, Determinantal varieties, Theta functions and abelian varieties, Families, moduli of curves (algebraic)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Complete intersections, Singularities of curves, local rings, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Fania, M. L. and Sommese, A. J. 'On the Minimality of Hyperplane Sections of Gorenstein Threefolds' (Preprint, January 1985). \(3\)-folds, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Families, moduli, classification: algebraic theory
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Gorla, E., Mixed ladder determinantal varieties from two-sided ladders, J. Pure Appl. Algebra, 211, 2, 433-444, (2007) Determinantal varieties, Linkage, complete intersections and determinantal ideals
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Vanishing theorems in algebraic geometry, Vector bundles on surfaces and higher-dimensional varieties, and their moduli
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties V. Lakshmibai and P. Shukla, Standard monomial bases and geometric consequences for certain rings of invariants, Proc. Indian Acad. Sci. Math. Sci. 116 (2006), 9--36. Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Actions of groups on commutative rings; invariant theory, Classical groups (algebro-geometric aspects), Grassmannians, Schubert varieties, flag manifolds, Rings with straightening laws, Hodge algebras
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Aberbach I. and Huneke, C. : An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees rings , Math. Ann. 297 (1993) 343-369. Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure, Cohen-Macaulay modules, Regular local rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties \beginbarticle \bauthor\binitsA. S. \bsnmBuch, \batitleAlternating signs of quiver coefficients, \bjtitleJ. Amer. Math. Soc. \bvolume18 (\byear2005), page 217-\blpage237. \endbarticle \OrigBibText ----, Alternating signs of quiver coefficients , J. Amer. Math. Soc. 18 (2005), 217-237. \endOrigBibText \bptokstructpyb \endbibitem Grassmannians, Schubert varieties, flag manifolds, Determinantal varieties, \(K\)-theory of schemes
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties M. Andreatta and A.J. Sommese,On the projective normality of the adjunction bundles, Comm. Math. Elv.66 (1991), 362--367 Projective techniques in algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Bongartz, K.: Minimal singularities for representations of Dynkin quivers. Comment. Math. Helv. 69(4), 575--611 (1994) Representations of quivers and partially ordered sets, Representation type (finite, tame, wild, etc.) of associative algebras, Group actions on varieties or schemes (quotients), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Singularities in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Morales, M.: Équations des variétés monomiales en codimension deux. J. algebra 175, 1082-1095 (1995) Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Low codimension problems in algebraic geometry
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Wheeler, A.K.: Ideals generated by principal minors. http://arxiv.org/abs/1410.1910 (2015) Linkage, complete intersections and determinantal ideals, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Hashimoto, M.: Resolutions of determinantal ideals: t-minors of (t + 2) \({\times}\) n matrices. J. algebra 142, 456-491 (1991) Linkage, complete intersections and determinantal ideals, Determinantal varieties, Syzygies, resolutions, complexes and commutative rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio, Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals, J. Algebra, 471, 409-453, (2017) Vector spaces, linear dependence, rank, lineability, Multilinear algebra, tensor calculus, Linkage, complete intersections and determinantal ideals, Determinantal varieties, Semialgebraic sets and related spaces
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Oneta, A.; Zatini, E.: A Note on Complementary Modules, Duality and Reflexiveness. Comm. in Alg. 12, 2631-2641 (1984) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Other special types of modules and ideals in commutative rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Auslander, M; Reiten, I, Almost split sequences for rational double points, Trans. Am. Math. Soc., 302, 87-97, (1987) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Singularities in algebraic geometry, Representation theory of associative rings and algebras, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Marie-Amélie Bertin, On the regularity of varieties having an extremal secant line, J. Reine Angew. Math. 545 (2002), 167 -- 181. Projective techniques in algebraic geometry, Syzygies, resolutions, complexes and commutative rings, \(n\)-folds (\(n>4\)), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Izelgue, L; Karim, D, On the imbedding into a product of zero-dimensional commutative rings, Commun. Algebra, 30, 5123-5133, (2002) Extension theory of commutative rings, Dimension theory, depth, related commutative rings (catenary, etc.), Local rings and semilocal rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties O. Taussky, Nonsingular cubic curves as determinantal loci, J. Math. Phys. Sci. 21 (1987), 665--678. Determinantal varieties, History of algebraic geometry, Vector and tensor algebra, theory of invariants, History of mathematics in the 19th century
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties M. Fontana, E. Houston, T. Lucas, \textit{Factoring Ideals in Integral Domains}, Lecture Notes of the Unione Matematica Italiana, Vol. 14, Springer, New York, 2013. Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial), Divisibility and factorizations in commutative rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Catanese, F., Cragnolini, P., Oliverio, P.: Surfaces with K2= =2, and special nets of quratics in 3-space. Contemp. Math. 162, 77--128 (1994) Surfaces of general type, Pencils, nets, webs in algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Linkage, complete intersections and determinantal ideals, \(K3\) surfaces and Enriques surfaces, \(3\)-folds, Fano varieties, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Laytimi F, On degeneracy loci, Int. J. Math. 7(6) (1996) 745--754 Vanishing theorems in algebraic geometry, Topological properties in algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Ponza, F.: On the Weierstrass weights at Gorenstein singularities. Lecture notes in pure and applied math 166, 129-136 (1994) Riemann surfaces; Weierstrass points; gap sequences, Singularities of curves, local rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties J. P. Jouanolou, Formes d'inertie et résultant: un formulaire, Adv. Math. 126 (1997), no. 2, 119 -- 250 (French). Actions of groups on commutative rings; invariant theory, Determinantal varieties, Polynomials over commutative rings, Complete intersections, Vector and tensor algebra, theory of invariants
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Tevelev, E. A., \textit{Projective Duality and Homogeneous Spaces}, 133, (2005), Springer-Verlag, Berlin Homogeneous spaces and generalizations, Projective techniques in algebraic geometry, Determinantal varieties, Group actions on varieties or schemes (quotients), Grassmannians, Schubert varieties, flag manifolds, Complete intersections
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Tchernev, A.: Acyclicity criteria for complexes associated with an alternating map. Proc. amer. Math. soc. 129, No. 10, 2861-2869 (2001) Syzygies, resolutions, complexes and commutative rings, Homological dimension and commutative rings, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties A. A. du Plessis and C. T. C. Wall, Singular hypersurfaces, versality, and Gorenstein algebras, J. Algebraic Geom. 9 (2000), no. 2, 309-322. Singularities of surfaces or higher-dimensional varieties, Local deformation theory, Artin approximation, etc., Hypersurfaces and algebraic geometry, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Hoa L.T. (1993). On minimal free resolutions of projective varieties of degree=codimension+2. J. Pure Appl. Algebra 87: 241--250 Syzygies, resolutions, complexes and commutative rings, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Linkage, complete intersections and determinantal ideals
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics, Cohen-Macaulay modules, Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties DOI: 10.1006/jabr.1996.6824 Homological dimension in associative algebras, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Cohen-Macaulay modules in associative algebras, Group rings
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Grassmannians, Schubert varieties, flag manifolds, Determinantal varieties, Homogeneous spaces and generalizations
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Gelfand, I. M.; Zelevinskiĭ, A. V.; Kapranov, M. M.: Projective-dual varieties and hyperdeterminants, Dokl. akad. Nauk SSSR 305, No. 6, 1294-1298 (1989) Low codimension problems in algebraic geometry, Determinantal varieties
0
O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Determinantal varieties Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
0