Eloise Hamilton (Oxford) -  Cohomology of GIT quotients, reductive and non-reductive
Channel: Jesús Martínez-García
Date: 2020-12-10

Eloise Hamilton (Oxford) -  Cohomology of GIT quotients, reductive and non-reductive

Talk delivered at EDGE 2020 (online) Workshop "Explicit K-stability and Moduli Problems".

https://www.maths.ed.ac.uk/cheltsov/edge2020/

Abstract: Geometric Invariant Theory (GIT) is a powerful tool not only for constructing quotients in algebraic geometry, but also for studying the geometry of these quotients. The aim of this talk is to explain how to calculate the (rational) cohomology of quotients constructed on the one hand using classical GIT, and on the other using a recent generalisation of GIT, called Non-Reductive GIT. As its name suggests, Non-Reductive GIT enables the construction of quotients by a certain class of non-reductive group actions. After reviewing existing methods for computing the Poincare series of classical GIT quotients when the initial variety is smooth, we will show how similar methods can be used to compute the Poincare series of non-reductive GIT quotients.