Algebraic Groups Seminar
Wednesday, 08/03/2023, 10.30 am
Venue: https://meet.google.com/jcn-nwpx-nmq
Host: Shripad M. Garge
Speaker: Arpita Nayek
Affiliation: IIT Bombay
Title: On the torus quotients of Schubert varieties in Grassmannians
Abstract: Let G=SO(8n, C) or SO(8n+4, C) and T be a maximal torus of G. Let P be the maximal parabolic subgroup of G corresponding to the simple root \alpha_{4n} (respectively, \alpha_{4n+2}). In the first part of the talk, we will discuss the projective normality of the GIT quotients of certain Schubert varieties in G/P with respect to a T-linearized very ample line bundle on G/P. Let G_{r,n} be the Grassmannian of all r-dimensional subspaces of C^n. For r and n coprime, let X(w_{r,n}) be the unique minimal dimensional Schubert variety in G_{r,n} admitting semi-stable points. Let X^v_{w_{r,n}} be the Richardson variety in G_{r,n} corresponding to the Weyl group elements v and w_{r,n}. In the second part of the talk, we will discuss the sufficient conditions on v such that the GIT quotient of X^v_{w_{r,n}} is the product of projective spaces. The first part of my talk is based on a joint work with Pinakinath Saha and the second part of my talk is based on a joint work with Somnath Dake and Shripad Garge.