Results 11 to 20 of about 175 (164)
Geometric vertex decomposition and liaison
Forum of Mathematics, Sigma, 2021 Geometric vertex decomposition and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this paper, we establish an explicit connection between these approaches.
Patricia Klein, Jenna Rajchgot
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Determinacy of determinantal varieties [PDF]
manuscripta mathematica, 2018 10 ...
Imran Ahmed, Maria Aparecida Soares Ruas
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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
Brandenburg, Marie Charlotte +2 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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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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Arcs on determinantal varieties [PDF]
Transactions of the American Mathematical Society, 2012 27 pages. This is part of the author's PhD thesis at the University of Illinois at Chicago. v2: Minor changes.
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On minimality of determinantal varieties [PDF]
Linear Algebra and its Applications, 2021 We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of real matrices of a given size.
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Two-dimensional gauge dynamics and the topology of singular determinantal varieties
Journal of High Energy Physics, 2017 We record an observation about the Witten indices in two families of gauged linear sigma models: the U(2) model for linear sections of Grassmannians, and the U(1) model for quadric complete intersections. We describe how the Witten indices are related to
Kenny Wong
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Determinantal Calabi-Yau varieties in Grassmannians and the Givental I-functions
Journal of High Energy Physics, 2018 We examine a class of Calabi-Yau varieties of the determinantal type in Grassmannians and clarify what kind of examples can be constructed explicitly.
Yoshinori Honma, Masahide Manabe
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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.
Gonciulea, Nicolae +1 more
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