Speaker: Victoria Hoskins from Freie University Berlin.
Title : Stratifications in moduli theory
Abstract
Many moduli spaces in algebraic geometry are constructed as quotients of algebraic varieties by a reductive group action using geometric invariant theory. In this talk we explain two such examples: moduli of coherent sheaves on a projective variety and moduli of quiver representations. In both cases, we introduce and compare two stratifications: a Harder-Narasimhan stratification associated to the notion of stability for the moduli problem and a stratification coming from the geometric invariant theory construction. In nice cases, these stratifications can be used to give recursive formulas for the Betti numbers of the moduli spaces.
Poster: http://www.math.iitb.ac.in/~seminar/colloquium/colloq-13-oct-16.pdf
5:00pm
6:00pm
Time:
4:00pm-5:00pm
Location:
Ramanujan Hall
Description:
Speaker: Victoria Hoskins from Freie University Berlin.
Title : Stratifications in moduli theory
Abstract
Many moduli spaces in algebraic geometry are constructed as quotients of algebraic varieties by a reductive group action using geometric invariant theory. In this talk we explain two such examples: moduli of coherent sheaves on a projective variety and moduli of quiver representations. In both cases, we introduce and compare two stratifications: a Harder-Narasimhan stratification associated to the notion of stability for the moduli problem and a stratification coming from the geometric invariant theory construction. In nice cases, these stratifications can be used to give recursive formulas for the Betti numbers of the moduli spaces.