Seminar by Narasimha Chary (CMI, India)

Title: On Bott-Samelson-Demazure-Hansen Variety

2015.09.09 | Jane Jamshidi

Date Wed 16 Sep
Time 15:30 16:30
Location 1531-215 (Aud. D3)


Let G be a simple algebraic group of adjoint type over the field of complex numbers, let B be a Borel subgroup of G containing a maximal torus T of G, w be an element of the Weyl group W and X(w) be the Schubert variety in the flag variety G/B corresponding to w. Let Z(w; i) be the Bott-Samelson-Demazure-Hansen variety (the desingularization of the Schubert variety X(w)) corresponding to a reduced expression i of w.
In this talk, we will discuss the automorphism group of Z(w; i) and vanishing results for the cohomology of the tangent bundle of Z(w; i). As an application, we see that the varieties Z(w; i) are rigid when G is simply-laced and their deformations are unobstructed in general. Finally, I will state some results on GIT-quotients of the ag variety G/B by a maximal torus.