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arXiv · 1912.08618

Smooth torus quotients of Schubert varieties in the Grassmannian

Sarjick Bakshi·S. Senthamarai Kannan·K. Venkata Subrahmanyam
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Abstract

Let $r < n$ be positive integers and further suppose $r$ and $n$ are coprime. We study the GIT quotient of Schubert varieties $X(w)$ in the Grassmannian $G_{r,n}$, admitting semistable points for the action of $T$ with respect to the $T$-linearized line bundle ${\cal L}(n\omega_r)$. We give necessary and sufficient combinatorial conditions for the GIT quotient $T\backslash\mkern-6mu\backslash X(w)^{ss}_{T}({\cal L}(n\omega_r))$ to be smooth.

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Sarjick Bakshi, S. Senthamarai Kannan, K. Venkata Subrahmanyam. 2019-12-18. Smooth torus quotients of Schubert varieties in the Grassmannian. https://arxiv.org/abs/1912.08618

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