Prelectura de tesis

Nombre: Guillermo Barajas Ayuso

Director: Óscar García Prada

Tutor: Mario García Fernández

Lector: Emilio Franco Gómez

26 de abril, sala 520, módulo 17

15:30 hr.

Título de la tesis: Fixed points in Higgs bundle moduli spaces and the Prym-Narasimhan-Ramanan construction

Abstract: The aim of this thesis is the description of fixed points of some finite group actions on the moduli space of G-Higgs bundles over a compact Riemann surface X, where G is a connected semisimple complex Lie group with center Z. These actions involve rescaling the Higgs field, extending the structure group by automorphisms of G, "tensoring" by Z-bundles and pulling back by automorphisms of X. We find that simple fixed points correspond to Higgs pairs over certain étale covers of X equipped with an action of the respective Galois group. This generalizes the work of Narasimhan and Ramanan, who showed that vector bundles over X which are fixed by tensorization by a line bundle L of finite order are pushforwards of vector bundles over the étale cover associated to L. Our results also generalize previous work by García-Prada and Ramanan, who restrict themselves to cyclic group actions.