Results 1 to 10 of about 761 (218)
An algorithm for computing Schubert varieties of best fit with applications [PDF]
Frontiers in Artificial Intelligence, 2023 We propose the geometric framework of the Schubert variety as a tool for representing a collection of subspaces of a fixed vector space. Specifically, given a collection of l-dimensional subspaces V1, …, Vr of ℝn, represented as the column spaces of ...
Karim Karimov +2 more
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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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Staircase diagrams and the enumeration of smooth Schubert varieties [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert varieties are in bijection with a new combinatorial data ...
Edward Richmond, William Slofstra
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Total positivity for the Lagrangian Grassmannian [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The positroid decomposition of the Grassmannian refines the well-known Schubert decomposition, and has a rich combinatorial structure. There are a number of interesting combinatorial posets which index positroid varieties,just as Young diagrams index ...
Rachel Karpman
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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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The Prism tableau model for Schubert polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1; x2; : : :]. We suggest the prism tableau model for these polynomials.
Anna Weigandt, Alexander Yong
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Which Schubert varieties are local complete intersections? [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We characterize by pattern avoidance the Schubert varieties for $\mathrm{GL}_n$ which are local complete intersections (lci). For those Schubert varieties which are local complete intersections, we give an explicit minimal set of equations cutting out ...
Henning Úlfarsson, Alexander Woo
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Toroidal Schubert Varieties [PDF]
Algebras and Representation Theory, 2019 Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the toroidal and horospherical partial flag varieties with Picard number 1. In the more general case, we provide a set of necessary conditions for the action of a Levi subgroup on ...
Mahir Bilen Can +2 more
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Rational smoothness and affine Schubert varieties of type A [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 The study of Schubert varieties in G/B has led to numerous advances in algebraic combinatorics and algebraic geometry. These varieties are indexed by elements of the corresponding Weyl group, an affine Weyl group, or one of their parabolic quotients ...
Sara Billey, Andrew Crites
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$q$-Rationals and Finite Schubert Varieties
Comptes Rendus. Mathématique, 2023 The classical $q$-analogue of the integers was recently generalized by Morier-Genoud and Ovsienko to give $q$-analogues of rational numbers. Some combinatorial interpretations are already known, namely as the rank generating functions for certain ...
Ovenhouse, Nicholas
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