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arXiv · 1808.05918

The Nash blow-up of a cominuscule Schubert variety

Edward Richmond·William Slofstra·Alexander Woo
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Abstract

We compute the Nash blow-up of a cominuscule Schubert variety. In particular, we show that the Nash blow-up is algebraically isomorphic to another Schubert variety of the same Lie type. As a consequence, we give a new characterization of the smooth locus and, for Grassmannian Schubert varieties, determine when the Nash blow-up is a resolution of singularities. We also study the induced torus action on the Nash blow-up and give a bijection between its torus fixed points and Peterson translates on the Schubert variety.

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Edward Richmond, William Slofstra, Alexander Woo. 2018-08-17. The Nash blow-up of a cominuscule Schubert variety. https://arxiv.org/abs/1808.05918

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