Vicente Muñoz (CSIC, Madrid)

Moduli Spaces of Pairs and of Bundles

Pairs are objects formed by a holomorphic bundle over a compact Riemann surface, together with a holomorphic section. There is a concept of stability for pairs depending on a real parameter tau and we can consider moduli spaces of tau-stable pairs. We show how these moduli spaces are related to the moduli spaces of stable bundles, and how they do depend on tau. This gives a method to prove properties of the moduli spaces of bundles and of pairs, by induction on the rank.

We show many instances of this technique: irreducibility, birationality, Brauer class, stably rationality, Hodge structures, Torelli theorems, Hodge numbers, motives, Hodge conjecture, ...