Summer Lectures in Geometry 

25/06/2010, 11:00 — 12:30 — Room P3.10, Mathematics Building
Vicente Muñoz, Universidad Complutense de Madrid

Moduli spaces of pairs: Hodge-Deligne polynomials

We shall study moduli spaces of vector bundles over a complex curve, and moduli spaces of pairs formed by a vector bundle and a global section. There is a concept of stability for pairs which depends on a real parameter. These moduli spaces suffer a birational transformation when the parameter crosses certain critical values. We shall see how properties of the algebraic structure of the mentioned moduli spaces (such as Hodge numbers, Hodge structures, Torelli theorems) can be deduced from a careful study of these birational transformations.

We give the computation of Hodge-Deligne polynomials of the moduli spaces of pairs for small rank. This gives in particular the Poincaré polynomials of the moduli spaces. An analogous procedure allows to determine the K-theory class of these spaces.