Smooth torus quotients of Schubert varieties in the Grassmannian

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 $\mathcal{L}(n{\omega }_r)$. We give necessary and sufficient combinatorial conditions for the GIT quotient $T\backslash \backslash X(w{)}_T^{ss}(\mathcal{L}(n{\omega }_r))$ to be smooth.

Cited by in corpus (1)

• On the torus quotients of Schubert varieties