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arXiv · 2401.06317

Gorenstein toric Schubert varieties in Grassmannians

Shin-young Kim·Eunjeong Lee
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Abstract

A partial flag variety is a smooth projective homogeneous variety admitting an action of a maximal torus $T$. Schubert varieties are $T$-invariant subvarieties of the partial flag varieties. We study toric Schubert varieties in Grassmannian varieties with respect to the action of the torus $T$. Indeed, we present an explicit description of the fan of a Gorenstein toric Schubert variety in a Grassmannian, and we prove that any Gorenstein toric Schubert variety in a Grassmannian variety is Fano.

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Shin-young Kim, Eunjeong Lee. 2024-01-12. Gorenstein toric Schubert varieties in Grassmannians. https://arxiv.org/abs/2401.06317

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