text stringlengths 2 1.42k | label int64 0 1 |
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rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). algebraic computation; symbolic computation; rank Jacobian varieties; reduce | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). multilinear algebra; tensor products; algebraic varieties; secant varieties; representation theory; complexity theory; matrices; monograph; textbook; matrix multiplication; tensor decomposition; tensor network; border rank; tensor calculus; projective algebraic geometry; Terracini's Lemma; polynomial Waring problem; Segre varieties; signal processing; Littlewood-Richardson rule; Pieri's formula; Strassen's equation; Young flattening; Friedland's equation; Fano varieties of line; Chow varieties of zero cycle; Brill's equation; normal form; Konstant's theorem; Bott-Borel-Weil theorem; Koszul sequences; syzygies J. M. Landsberg, \textit{Tensors: Geometry and Applications}, American Mathematical Society, Providence, RI, 2012. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). bound on the degree of the rank 1 locus; map of vector bundles; determinantal loci; Castelnuovo theory; Clifford theory; products of linear series; Clifford index D. Eisenbud, J. Harris: An intersection bound for rank 1 loci, with applications to Castelnuovo and Clifford theory, J. Alg. Geom.1, 31--60 (1992) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). resolution of singularities; idealistic exponents; positive characteristic; determinantal varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). numerical multilinear algebra; tensors; multidimensional arrays; multiway arrays; tensor rank; tensor decompositions; low-rank tensor approximations; hyperdeterminants; Eckart-Young theorem; principal component analysis; parafac; candecomp; Brégman divergence of tensors V. de Silva and L.-H. Lim, \textit{Tensor rank and the ill-posedness of the best low-rank approximation problem}, SIAM J. Matrix Anal. Appl., 30 (2008), pp. 1084--1127, . | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). computer algebra; real algebraic geometry; determinantal varieties; algorithm; complexity D. Henrion, S. Naldi, and M. Safey El Din, \textit{Real root finding for determinants of linear matrices}, J. Symbolic. Comput., 74 (2016) pp. 205--238. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). relations of minors; determinantal varieties; plethysms Ronald King and Trevor Welsh, \textit{Some remarks on characters of symmetric groups, Schur functions, Littlewood-Richardson and Kronecker coefficients}, work in progress http://congreso.us.es/enredo2009/Workshop_files/Sevilla_King.pdf. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tensor rank; typical rank; tall tensor; semi-tall tensor; Bezout's theorem; determinantal variety | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). arithmetical rank; cohomological dimension; varieties of minimal degree; set theoretic complete intersection | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal ideals; Hilbert functions; determinantal varieties; Schubert varieties; ladder determinantal varieties; Hilbert series DOI: 10.1016/S0012-365X(01)00256-4 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). modular representations; elementary Abelian groups; modules of constant Jordan type; vector bundles; rank varieties; Chern classes; Frobenius twists; endotrivial modules Benson, D.: Modules for elementary abelian \(p\)-groups. In: Proceedings of the International Congress of Mathematicians (ICM 2010), pp. 113-124 (2010) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). derived categories; semiorthogonal decomposition; projectivization; flops; determinantal varieties; curves; nested Hilbert schemea | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). intresection cohomology; arc space; determinantal varieties; toric varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank 1 commutators; varieties of matrices; Zariski topology; commutators; irreducible components Michael G. Neubauer, The variety of pairs of matrices with rank(\?\?-\?\?)\le 1, Proc. Amer. Math. Soc. 105 (1989), no. 4, 787 -- 792. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal rings; secant varieties Conca, A.; Mostafazadehfard, M.; Singh, A. K.; Varbaro, M., Hankel determinantal rings have rational singularities, Adv. Math., 335, 111-129, (2018) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). strength; polynomial functor; infinite tensors; GL-varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). algebraic geometry; tensor analysis; symmetric tensors; Veronese varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). jet schemes; Hilbert series; determinantal varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). cohomolgical rank functions; syzygies of primitive embeddings; abelian varieties; generic vanishing | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank of the Néron-Severi group; Prym varieties; intermediate Jacobian; infinitesimal variation of Hodge structure Pirola, G.P.: Base number theorem for Abelian varieties. Math. Ann.282, 361--368 (1988) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). homomorphic sensing; unlabeled sensing; linear regression without correspondences; Jordan form; determinantal varieties; rational normal scrolls | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Gröbner basis; degenerations of Schubert varieties; flag variety; toric varieties; determinantal varieties Lakshmibai, V., Degenerations of flag varieties to toric varieties.C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), 1229--1234. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). quantum matrices; quantum Grassmannians; quantum Schubert varieties; quantum determinantal rings; straightening laws Lenagan, T. H.; Rigal, L., Quantum graded algebras with a straightening law and the \textit{AS}-Cohen-Macaulay property for quantum determinantal rings and quantum Grassmannians, J. Algebra, 301, 2, 670-702, (2006) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). effective divisors; families of sheaves; abelian integrals; Picard variety; cohomology of sheaves; variation of cohomology; determinantal varieties; theta divisor Kempf, George, Abelian integrals, Monografías del Instituto de Matemáticas [Monographs of the Institute of Mathematics] 13, vii+225 pp., (1983), Universidad Nacional Autónoma de México, México | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; irreducible decomposition; Ehresmann partial order | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). ladder determinantal varieties Narasimhan, H.: The irreducibility of ladder determinantal varietiés. J. algebra 102, 162-185 (1986) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Young tableaux; straightening law; ladder determinantal varieties Sudhir R. Ghorpade, Abhyankar's work on Young tableaux and some recent developments, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 215 -- 249. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant varieties; Segre-Veronese varieties; defective varieties; Horace method; partially symmetric tensors H. Abo and M. Brambilla, \textit{On the dimensions of secant varieties of Segre-Veronese varieties}, Ann. Mat. Pura Appl. (4), 192 (2013), pp. 61--92. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). higher dimensional varieties free of general type; pluriregular; hypersurfaces; classification; determinantal variety; canonical ring Catanese, F.: Equations of pluriregular varieties of general type. Progr. math. 60, 47-67 (1985) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). survey; path model; representation theory; complex semisimple algebraic groups; ladder determinantal varieties; canonical bases; Schubert varieties; quiver varieties; Bott-Samelson varieties Venkatramani Lakshmibai, Peter Littelmann, and Peter Magyar, Standard monomial theory and applications, Representation theories and algebraic geometry (Montreal, PQ, 1997) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 514, Kluwer Acad. Publ., Dordrecht, 1998, pp. 319 -- 364. Notes by Rupert W. T. Yu. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). border rank; complexity of matrix multiplication; secant varieties Landsberg, J.M.: Geometry and the complexity of matrix multiplication. Bull. Am. Math. Soc. (N.S.) \textbf{45}(2), 247-284 (2008) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). \(D\)-modules; Hodge modules; Hodge filtration; pole order filtration; logarithmic differential forms; simple normal crossing divisors; complements of hypersurfaces; de Rham complex; \(b\)-function; polarized abelian varieties; ample divisors; theta divisors; Prym varieties; semiquasihomogeneous isolated singularities; generic determinantal hypersurfaces; vanishing criteria; Kodaira vanishing theorem; Akizuki-Nakano vanishing theorem; Nadel vanishing theorem; Griffiths vanishing theorem; Artin vanishing theorem | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Young tableaux; Schubert varieties; determinantal ideals; bitableau; binomial coefficients; invariant theory; multitableaux S. S. Abhyankar, Enumerative Combinatorics of Young Tableaux, Marcel Dekker, New York, 1988. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant varieties; Segre embedding; border rank; numerical algebraic geometry; representation theory Bates, DJ; Oeding, L, Toward a salmon conjecture, Exp Math, 20, 358-370, (2011) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; arc schemes; minimal log discrepancy | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Artinian algebra; parametrization; Hilbert function; homology; Artinian quotients; Grassmannian varieties; determinantal variety; Hankel matrix; homology class of intersection Iarrobino, A., Yameogo, J.: The family \(G\)\_{}\{\(T\)\} of graded quotients of \({k[x,y]}\) of given Hilbert function. arXiv:alg-geom/9709021 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). low-rank matrices; determinantal variety; set convergence; inner and outer limits; set-valued mappings; inner and outer semicontinuity; tangent and normal cones | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Selmer group; Mordell-Weil rank; Brauer-Severi varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). path algebras; maximal rank of homomorphisms; quivers; finitely generated right modules; dimension vectors; Grassmann varieties; bilinear forms; affine varieties; configuration spaces of representations; finitely presented right modules; simple Artinian rings Crawley-Boevey, W, On homomorphisms from a fixed representation to a general representation of a quiver, Trans. Am. Math. Soc., 348, 1909-1919, (1996) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant varieties; Segre varieties; tensor algebra; hypermatrices; tensor rank; border rank H. Abo, G. Ottaviani, and C. Peterson, \textit{Induction for secant varieties of Segre varieties}, Trans. Amer. Math. Soc., 361 (2009), pp. 767--792, . | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; Veronese variety; catalecticant matrices Pucci, M., The Veronese variety and catalecticant matrices, J. Algebra, 202, 1, 72-95, (1998) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). collineation bundle; determinantal varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). theta characteristic; determinantal varieties W. M. Oxbury, Theta-characteristic-valued endomorphisms of a stable bundle , | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). ternary cubics; rank; border rank; cubic forms; symmetric tensors; typical rank; Waring rank; De Paolis algorithm Banchi, M.: Rank and border rank of real ternary cubics. Boll. Unione Mat. Ital. \textbf{8}(1), 65-80, 14N05 (14H50 14Q05) (2015) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). jet schemes; Pfaffian varieties; determinantal ideals; irreducible varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). algebraic family of curves; resultants; determinantal varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). k-equivalence; germs of complex analytic varieties with isolated singular points; real-analytic equivalence; embedding dimension; rank; order | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). 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) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). non-commutative resolution; determinantal varieties; derived category; noncommutative crepant resolution (NCCR); NCCR; Springer resolution; symplectic group Špenko, Š.; Van den Bergh, M., Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices, (2015), preprint | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Lipschitz function; descent direction; Clarke subdifferential; algebraic varieties; Riemannian manifolds; robust low-rank matrix recovery | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). average rank of the Mordell-Weil group of abelian varieties; Lefschetz pencil | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). real algebraic geometry; real quadrics; homological compexity; determinantal varieties Lerario, A, Complexity of intersections of real quadrics and topology of symmetric determinantal varieties, J. Eur. Math. Soc. (JEMS), 18, 353-379, (2016) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Equivariant Chow ring; wonderful symmetric varieties of minimal rank; Chern classes Brion, M; Joshua, R, Equivariant Chow ring and Chern classes of wonderful symmetric varieties of minimal rank, Transform. Groups, 13, 471-493, (2008) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Gorenstein varieties; Cohen-Macaulay modules; syzygies; regular; surfaces of general type; quasi-generic canonical projections; moduli problems; canonical ring; determinantal singularities Catanese, F.: Commutative algebra methods and equations of regular surfaces. (Lect. Notes Math., vol. 1056, pp. 68-111). Berlin Heidelberg New York: Springer 1984 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). syzygies of determinantal varieties P. Pragacz and J. Weyman, Resolutions of determinantal varieties; a survey, in ''Lecture Notes in Math.,'' Vol. 1220, Springer-Verlag, New York/Berlin. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). algebraic geometry; projective varieties; algebraic curves; algebraic surfaces; determinantal varieties; Cremona transformations; del Pezzo surfaces; theta characteristics; Grassmannians; line complexes Dolgachev, I. V.: \textit{Classical algebraic geometry. A modern view. }Cambridge University Press, Cambridge, 2012. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). 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. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Hilbert polynomial of the homogeneous coordinate rings of Schubert; varieties in the Grassmann manifold; big cell; bi-tableaux; determinantal varieties; Hilbert polynomial of the homogeneous coordinate rings of Schubert varieties in the Grassmann manifold Galligo, A.: Computations of some Hilbert functions related with Schubert calculus. Lecture notes in mathematics 1124 (1985) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). vector bundles; determinantal representations; hyperbolic varieties; real algebraic geometry | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Pfaffian representations; cubic surfaces; ACM sheaves; determinantal varieties Tanturri, F.: Pfaffian representations of cubic surfaces. Geom. Dedicata (2013). 10.1007/s10711-012-9818-x | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tropical geometry; tropical convexity; secant varieties; rank; symmetric matrices; hypergraph coloring | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tropical geometry; determinantal varieties; shellability Markwig, H.; Yu, J.: The space of tropically collinear points is shellable, Collect. math. 60, No. 1, 63-77 (2009) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Pfaffian ideals; determinantal ideal; étale cohomology; Poincaré duality; homogeneous ideal of a polynomial ring; arithmetical rank | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). join varieties; polynomial forms; determinantal representation Chiantini, L., Geramita, A.V.: On the determinantal representation of quaternary forms. Commun. Alg. \textbf{42}, 4948-4954 (2014) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). correspondences; quadrics; moduli spaces; Chow varieties; Hilbert varieties; geometric invariant theory; algebraic groups; Grassmannians; cones; determinantal varieties; maps; degree; dimension; smoothness J.~Harris, \textit{Algebraic geometry: a first course}, Graduate Texts in Mathematics \textbf{133}, Springer-Verlag, New York, 1992. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Mordell-Weil rank; families of abelian varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant varieties of curves; jumping line; rank 2 vector bundle Gruson, L.; Peskine, C., Courbes de l'espace projectif: variétés de sécantes, (Enumerative Geometry and Classical Algebraic Geometry, Nice, 1981, Progr. Math., vol. 24, (1982), Birkhäuser Boston), 1-31 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal loci; regular intersections of hypersurfaces; Euler characteristic; Todd genus; signature; determinantal varieties; incomplete intersections | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). orbit closures; representations; connected reductive groups; rank varieties; symmetric matrices; anti-symmetric matrices; orthogonal matrix; symplectic matrix Lovett, S. T.: Orthogonal and symplectic analogues of determinantal ideals. J. algebra 291, 416-456 (2005) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). group of automorphisms of smooth curve; \(L\)-functions; zeta-functions; Galois covering; class numbers; varieties over finite fields; Betti numbers; rank of the Mordell-Weil group; conjectures of Birch-Swinnerton-Dyer; Tate conjectures on algebraic cycles Kani, No article title, J. Number Theory, 46, 230, (1994) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Jacobian varieties; elliptic curves; rank | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Segre-Veronese varieties; rank of polynomials | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). multilinear algebra; tensor rank; determinantal schemes S. P. Diaz and A. Lutoborski, \textit{Polynomial foldings and tensor ranks}, J. Commut. Algebra, 8 (2016), pp. 173--206. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). local cohomology; determinantal varieties; polynomial functions; GL-invariant ideals Raicu, Claudiu, Regularity and cohomology of determinantal thickenings, Proc. Lond. Math. Soc. (3), 116, 2, 248-280, (2018) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; projective techniques; varieties defined by ring conditions S. M. Cooper and S. P. Diaz, \textit{The Gale transform and multi-graded determinantal schemes}, J. Algebra, 319 (2008), pp. 3120--3127. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Schubert varieties; singular loci; roots; Weyl groups; tangent cone; parabolic groups; Bruhat-Chevalley orders; grassmannian; Kazhdan-Lusztig polynomials; classical groups; nil-Hecke ring; minuscule groups; Poincaré polynomial; determinantal varieties; Dynkin diagrams 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 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant variety; \(X\)-rank; tangential variety; join of two varieties; Segre variety; tensor rank | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). additive decompositions; secant varieties; Veronese varieties; Segre varieties; Segre-Veronese varieties; Grassmannians; tensor rank; Waring rank; algorithm | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Segre varieties; tensor rank; tensor decomposition | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). toric varieties; arithmetical rank; complete intersections; semigroups M. Barile, Almost set-theoretic complete intersections in characteristic zero, 2005 (preprint), arXiv:math.AG/0504052 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). gentle algebras; bound quiver algebras; module varieties; moduli spaces of modules; rank sequences; rational invariants; up and down graphs; tame representation type; Schofield semi-invariants Carroll, Andrew T.; Chindris, Calin, On the invariant theory for acyclic gentle algebras, Trans. Amer. Math. Soc., 367, 5, 3481-3508, (2015) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Grassmannian; secant varieties; skew-symmetric tensors Hirotachi Abo, Giorgio Ottaviani & Chris Peterson, ``Non-defectivity of Grassmannians of planes'', J. Algebr. Geom.21 (2012) no. 1, p. 1-20 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). lattice ideal; toric varieties; arithmetical rank Katsabekis, A.; Morales, M.; Thoma, A., Binomial generation of the radical of a lattice ideal, J. Algebra, 324, 6, 1334-1346, (2010) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; sparse parameters; Noether complexity; Plücker coordinates; Chow form Glassbrenner, D.; Smith, K. E.: Sparse systems of parameters for determinantal varieties. Adv. in appl. Math. 19, 529-558 (1997) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; connectedness of degeneracy loci; Lefschetz-type theorems; Brill-Noether theory; constant period map [Tu] Tu, L.: Degeneracy loci. Proceedings, Berlin 1985, Teubner Verlag, Leipzig, 296--305 (1986) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Fano varieties; Picard rank; quasi-elementary contractions Grothendieck, A.: Le groupe de Brauer I, II, III. Exemples et compléments. In: Dix Exposés Sur La Coho- Mologie Des Schémas. North-Holland, Amsterdam, pp. 46-188 (1968) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). hyperelliptic curve; number of rational points; base changed curve; rank of twists of constant abelian varieties C. Schoen, ''Bounds for rational points on twists of constant hyperelliptic curves,''J. Reine Angew. Math.,411, 196--204 (1990). | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Waring rank; tensor rank; secant varieties De Paris, A.: A proof that the maximum rank for ternary quartics is seven. Matematiche (Catania) \textbf{70}(2), 3-18 (2015). 10.4418/2015.70.2.1 | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank; secant varieties; rational normal curves; projections Ballico, E.; Bernardi, A., On the \textit{X}-rank with respect to linear projections of projective varieties, Math. Nachr., 284, 17-18, 2133-2140, (2011) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). apolarity; real rank boundary; tensors; hyperdeterminants | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Fano varieties; Picard rank Casagrande, C, Numerical invariants of Fano 4-folds, Math. Nachr., 286, 1107-1113, (2013) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties Gorla, E., Mixed ladder determinantal varieties from two-sided ladders, J. Pure Appl. Algebra, 211, 2, 433-444, (2007) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). secant varieties; \(X\)-rank; cuspidal curve; rational normal curves; linear projections; border rank | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). invariants; determinantal varieties; standard monomials 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. | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tensor rank; typical rank; determinantal ideal; real radical; bilinear map; monomial preorder Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio, Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals, J. Algebra, 471, 409-453, (2017) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank varieties; Gorenstein varieties; varieties of square matrices; rank sets; rational singularities Eisenbud, D., Saltman, D.: Rank varieties of matrices, in Commutative Algebra (Berkeley, : MSRI Publ. 15. Springer-Verlag, New York \textbf{1989}, 173-212 (1987) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank of tensors; maximal rank; three-fold tensor Lavrauw, M.; Pavan, A.; Zanella, C.: On the rank of \(3{\times}3{\times}\)3-tensors, Linear multilinear algebra 61, No. 5, 646-652 (2013) | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). admissible rank; typical labels; semialgebraic sets; real algebraic varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Schubert varieties; affine flag varieties; determinantal varieties | 0 |
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Cremona transformation; determinantal variety; birational properties; arithmetically Cohen-Macaulay varieties | 0 |
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