Tuesday, March 05, 2024, 04:30pm - 05:30pm
In this talk, we discuss how GIT quotients by reductive groups depend on a choice of linearisation of the action, known as variation of GIT, by following the works of Thaddeus and Dolgachev-Hu. To this end, we shall discuss that there is a finite wall-and-chamber decomposition of the cone of linearisations such that the GIT quotient does not change when varying the linearisation in a chamber, and undergoes a blow-up blow-down transformation, similar to a Mori flip, when crossing adjacent chambers. Furthermore, we shall illustrate the birational transformations between the GIT quotients produced by wall-crossings in explicit toric situations. In the following week, we shall discuss wall crossings for certain degenerations of logarithmic Hilbert scheme of points.
Location: PMA 11.176