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arXiv · 2306.15323

Torus Quotients of Richardson Varieties

Somnath Dake·Shripad M. Garge·Arpita Nayek
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Abstract

For $1\le r\le n-1,$ let $G_{r,n}$ denote the Grassmannian parametrizing $r$-dimensional subspaces of $\mathbb{C}^{n}.$ Let $(r,n)=1.$ In this article we show that the GIT quotients of certain Richardson varieties in $G_{r,n}$ for the action of a maximal torus in $SL(n,\mathbb{C})$ are the product of projective spaces with respect to the descent of a suitable line bundle.

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Somnath Dake, Shripad M. Garge, Arpita Nayek. 2023-06-27. Torus Quotients of Richardson Varieties. https://arxiv.org/abs/2306.15323

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