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arXiv · 1807.04879

Toroidal Schubert Varieties

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.

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Mahir Bilen Can, Reuven Hodges, Venkatramani Lakshmibai. 2018-07-13. Toroidal Schubert Varieties. https://arxiv.org/abs/1807.04879

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