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arXiv · 2012.08102

On the torus quotients of Schubert varieties

Narasimha Chary Bonala·Santosha Kumar Pattanayak
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Abstract

In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in the smooth locus. As a consequence, we study the smoothness of torus quotients of Schubert varieties in the Grassmannian. We also prove that the torus quotient of any Schubert variety in the homogeneous space $SL(n, \mathbb C)/P$ is projectively normal with respect to the line bundle $\mathcal L_{\alpha_0}$ and the quotient space is a projective space, where the line bundle $\mathcal L_{\alpha_0}$ and the parabolic subgroup $P$ of $SL (n, \mathbb C)$ are associated to the highest root $\alpha_0$.

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Narasimha Chary Bonala, Santosha Kumar Pattanayak. 2020-12-15. On the torus quotients of Schubert varieties. https://doi.org/10.1142/s0129167x20501232

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