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arXiv · 1901.01043

Torus quotients of Richardson varieties in the Grassmannian

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

We study the GIT quotient of the minimal Schubert variety in the Grassmannian admitting semistable points for the action of maximal torus $T$, with respect to the $T$-linearized line bundle ${\cal L}(n ω_r)$ and show that this is smooth when $gcd(r,n)=1$. When $n=7$ and $r=3$ we study the GIT quotients of all Richardson varieties in the minimal Schubert variety. This builds on previous work by Kumar \cite{kumar2008descent}, Kannan and Sardar \cite{kannan2009torusA}, Kannan and Pattanayak \cite{kannan2009torusB}, and recent work of Kannan et al \cite{kannan2018torus}. It is known that the GIT quotient of $G_{2,n}$ is projectively normal. We give a different combinatorial proof.

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Sarjick Bakshi, S. Senthamarai Kannan, K. Venkata Subrahmanyam. 2019-01-04. Torus quotients of Richardson varieties in the Grassmannian. https://arxiv.org/abs/1901.01043

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