Intersection cohomology of the moduli spaces of stable bundles

28.03.2023 15:15 – 17:00

Intersection cohomology is a topological notion adapted to the description of singular topological spaces. The Decomposition Theorem for maps of algebraic varieties is a key tool in the subject, generalizing the Leray-Hirsch theorem.

The study of the intersection cohomology of the moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the work of Mozgovoy and Reineke, in joint work with Camilla Felisetti and Olga Trapeznikova, we give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map. We also give a new formula for the intersection Betti numbers of these moduli spaces, which has a clear geometric meaning. In these talk, I will give an introduction to the subject, and describe our results.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre