Torus quotients of Richardson varieties in the Grassmannian

2019/01/04 by Bakshi, Sarjick, Kannan, S. Senthamarai, Subrahmanyam, K. Venkata
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1901.01043

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 \citekumar2008descent, Kannan and Sardar \citekannan2009torusA, Kannan and Pattanayak \citekannan2009torusB, and recent work of Kannan et al \citekannan2018torus. It is known that the GIT quotient of G_2,n is projectively normal. We give a different combinatorial proof.

Related

• Smooth torus quotients of Schubert varieties in the Grassmannian
• Torus Quotients of Richardson Varieties
• Torus quotient of Richardson varieties in Orthogonal and Symplectic Grassmannians
• Smooth torus quotients of Richardson varieties in the Grassmannian
• GIT quotient of Schubert varieties modulo one dimensional torus