Date: Tuesday, December 22, 2020
Time: 3:30 PM .
Zoom Meeting Link:
https://us02web.zoom.us/j/85923312360?pwd=aFk5R2Z1alJ6dEV0UlBHQkV2aU84dz09
Meeting ID: 859 2331 2360
Passcode: 392843
Torus quotients of Schubert varieties in the Grassmannian $G_{2,n}$
Arpita Nayek
Chennai Mathematical Institute.
22-12-20

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Abstract

For the action of a maximal torus $T$ of $SL(n,C)$ on the Grassmannian $G_{r,n},$ the set of all $r$ dimensional subspaces of $C^n,$ the geometry (both symplectic and algebraic) of the GIT quotient $G_{r,n}//T$ have been extensively studied in recent years; Allen Knuston called them weight varieties in his thesis.

In this talk we consider the action of $T$ on $G_{2,n},$ where $n$ is a positive even integer. Here we study the GIT quotients of the Schubert varieties in the Grassmannian $G_{2,n}.$ We prove that the GIT quotient of the minimal dimensional Schubert variety in $G_{2,n}$ admitting stable points is the projective space $\mathbb{P}^{\mathfrak{n}{2}-1}.$ Further, we prove that the GIT quotients of the Schubert varieties in $G_{2,n}$ have finite singularities.

This is a joint work with Professor S. Senthamarai Kannan and Dr. Pinakinath Saha.