Results 11 to 20 of about 461,416 (208)
Singularities of Affine Schubert Varieties [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type A_l^{(1)}). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent ...
Jochen Kuttler, Venkatramani Lakshmibai
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An equivariant rim hook rule for quantum cohomology of Grassmannians [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A driving question in (quantum) cohomology of flag varieties is to find non-recursive, positive combinatorial formulas for expressing the quantum product in a particularly nice basis, called the Schubert basis.
Elizabeth Beazley +2 more
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Beilinson–Drinfeld Schubert varieties and global Demazure modules
Forum of Mathematics, Sigma, 2021 We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson–Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules over the current Lie algebra.
Ilya Dumanski +2 more
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Schubert varieties, inversion arrangements, and Peterson translation [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We show that an element $\mathcal{w}$ of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement $\mathcal{I} (\mathcal{w})$ associated to the inversion set of \mathcal{w} is inductively free, and the product $(d_1+1) ...(d_l+
William Slofstra
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A noncommutative geometric LR rule [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian.
Edward Richmond +2 more
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Diagonal degenerations of matrix Schubert varieties [PDF]
, 2023 Knutson and Miller (2005) established a connection between the anti-diagonal Gr\"obner degenerations of matrix Schubert varieties and the pre-existing combinatorics of pipe dreams. They used this correspondence to give a geometrically-natural explanation
Klein, Patricia
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On the torus quotients of Schubert varieties [PDF]
, 2021 In this paper, we consider the GIT quotients of Schubert varieties for theaction of a maximal torus. We describe the minuscule Schubert varieties forwhich the semistable locus is contained in the smooth locus.
Bonala, N., Pattanayak, S.
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Root-theoretic Young Diagrams, Schubert Calculus and Adjoint Varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 Root-theoretic Young diagrams are a conceptual framework to discuss existence of a root-system uniform and manifestly non-negative combinatorial rule for Schubert calculus.
Dominic Searles, Alexander Yong
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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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Chevalley-Monk and Giambelli formulas for Peterson Varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 A Peterson variety is a subvariety of the flag variety $G/B$ defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows.
Elizabeth Drellich
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