Summer Lectures in Geometry 

23/06/2010, 11:00 — 12:30 — Room P3.10, Mathematics Building
Vicente Muñoz, Universidad Complutense de Madrid

Moduli spaces of pairs: moduli spaces of pairs and of bundles

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 shall describe the moduli spaces of pairs, its relationship with the moduli of bundles, with emphasis on the role of the stability parameter and the birational transformations which happen when varying it, which are called flips.