Results 11 to 20 of about 27,072 (238)
DEGENERATE SCHUBERT VARIETIES IN TYPE A [PDF]
Transformation Groups, 2020 We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert variety associated to a rectangular element is indeed a Schubert variety in a partial flag variety of the same type with larger rank. Moreover, the degenerate Demazure module associated to a rectangular element
Chirivì Rocco +2 more
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On the Torus quotients of Schubert varieties [PDF]
International Journal of Mathematics, 2021 In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in the smooth locus. As a consequence, we study the smoothness of torus quotients of Schubert varieties in the Grassmannian. We also prove that the torus quotient
Narasimha Chary Bonala +1 more
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UNIVERSAL GRAPH SCHUBERT VARIETIES [PDF]
Transformation Groups, 2021 We consider the loci of invertible linear maps $f : \mathbb{C}^n \to {(\mathbb{C}^n)}^*$ together with pairs of flags $(E_\bullet, F_\bullet)$ in $\mathbb{C}^n$ such that the various restrictions $f : F_j \to E_i^*$ have specified ranks. Identifying an invertible linear map with its graph viewed as a point in a Grassmannian, we show that the closures ...
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On Tangent Cones of Schubert Varieties [PDF]
Arnold Mathematical Journal, 2017 We consider tangent cones of Schubert varieties in the complete flag variety, and investigate the problem when the tangent cones of two different Schubert varieties coincide. We give a sufficient condition for such coincidence, and formulate a conjecture that provides a necessary condition.
Fuchs, Dmitry +3 more
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Toric matrix Schubert varieties and root polytopes (extended abstract) [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Start with a permutation matrix π and consider all matrices that can be obtained from π by taking downward row operations and rightward column operations; the closure of this set gives the matrix Schubert variety Xπ.
Laura Escobar, Karola Mészáros
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Schubert Varieties and Free Braidedness [PDF]
Transformation Groups, 2004 We give a simple necessary and sufficient condition for a Schubert variety $X_w$ to be smooth when $w$ is a freely braided element of a simply laced Weyl group; such elements were introduced by the authors in a previous work (math.CO/0301104). This generalizes in one direction a result of Fan concerning varieties indexed by short-braid avoiding ...
Green, R. M., Losonczy, J.
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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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