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Mathematics > Algebraic Geometry

arXiv:1807.04879 (math)
[Submitted on 13 Jul 2018 (v1), last revised 13 Aug 2019 (this version, v3)]

Title:Toroidal Schubert Varieties

Authors:Mahir Bilen Can, Reuven Hodges, Venkatramani Lakshmibai
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Abstract: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 a Schubert variety to be toroidal. The singular locus of a (co)minuscule Schubert variety is shown to contain all the $L_{max}$-stable Schubert subvarieties, where $L_{max}$ is the standard Levi subgroup of the maximal parabolic which acts on the Schubert variety by left multiplication. In type A, the effect of the Billey-Postnikov decomposition on toroidal Schubert varieties is obtained.
Comments: To appear in Algebras and Representation Theory
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
Cite as: arXiv:1807.04879 [math.AG]
  (or arXiv:1807.04879v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.04879

Submission history

From: Mahir Bilen Can [view email]
[v1] Fri, 13 Jul 2018 01:17:50 UTC (25 KB)
[v2] Wed, 17 Jul 2019 02:35:42 UTC (21 KB)
[v3] Tue, 13 Aug 2019 01:14:26 UTC (21 KB)
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