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Room P3.10, Mathematics Building
Vicente Muñoz, Universidad Complutense de Madrid
Moduli spaces of pairs: Hodge structures
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 study more specific properties of the algebraic structure of the moduli spaces, like the (mixed) Hodge structures.