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Toric double determinantal varieties [PDF]
Communications in Algebra, 2021 Undergraduate ...
Alexander Blose +3 more
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The minimality of determinantal varieties [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2020 Abstract The determinantal variety Σ p q
Bordemann, Martin +2 more
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Jacobi–Trudi formulas and determinantal varieties [PDF]
Algebraic Combinatorics, 2023 Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi–Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.
Sam, Steven V, Weyman, Jerzy
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Tropical positivity and determinantal varieties
Algebraic Combinatorics, 2023 We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We focus on the study of low-rank matrices, in particular matrices of rank 2 and 3.
Brandenburg, Marie Charlotte +2 more
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Determinacy of determinantal varieties [PDF]
manuscripta mathematica, 2018 10 ...
Imran Ahmed, Maria Aparecida Soares Ruas
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Schubert varieties, toric varieties and ladder determinantal varieties [PDF]
Annales de l'Institut Fourier, 1997 We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai &
Gonciulea, Nicolae +1 more
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On Determinantal Varieties of Hankel Matrices [PDF]
Algebra, 2014 Let ℌ be a class of n×n Hankel matrices HA whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field 𝔽q. For every matrix in ℌ, it is shown that the varieties specified by the leading minors of orders from 1 to n-1 have the same number qn-1 of points in 𝔽qn.
Edoardo Ballico, Michele Elia
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The Representation Type of Determinantal Varieties [PDF]
Algebras and Representation Theory, 2017 This is a postprint (AAM) of an article published in Algebras and Representation Theory.
Kleppe, Jan O. +1 more
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Mixed Ladder Determinantal Varieties
Journal of Algebra, 2000 The authors generalize the notion of ladder determinantal varieties, which was introduced by Abhyankar, by allowing ideals of minors of different size of a matrix of indeterminates. Then they explore the relation between these mixed ladder determinantal varieties and Schubert varieties. Next they show that, up to product by affine spaces, each of these
Gonciulea, Nicolae, Miller, Claudia
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Non-commutative desingularization of determinantal varieties I [PDF]
Inventiones mathematicae, 2010 We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension.
Buchweitz, Ragnar-Olaf +2 more
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