Torus quotients of Richardson varieties in the Grassmannian

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 and show that this is smooth when When n = 7 and r = 3 we study the GIT quotients of all Richardson varieties in the minimal Schubert variety. This builds on work by Kumar [21], Kannan and Sardar [18], Kannan and Pattanayak [17], and Kannan et al. [16]. It is known that the GIT quotient of is projectively normal. We give a different combinatorial proof.