The study of spectral data for Higgs bundles goes back to Hitchin, who proved that, given a classic complex Lie group G, the fibers of the Hitchin map for the moduli space of G-Higgs bundles are Prym varieties of the Jacobian of the so called spectral curve. When G is an arbitrary complex reductive Lie group, the right notion it that of cameral covers. This was understood by several authors, including Donagi and Gaitsgory, who give a universal and complete description of the Hitchin fibration for the stack of G-Higgs pairs, proving it to be an abelian gerbe over the Hitchin base. After reviewing some preliminary material on real forms and gerbes, I will explain Donagi and Gaitsgory's work, and how their ideas can be adapted to the case of real forms. In particular, I will prove that given a real form G of a complex reductive algebraic group G^c, the stack of G-Higgs bundles is a gerbe over the corresponding Hitchin base. When the form is quasi-split, the gerbe is abelian and admits a simpler description. Time permitting, I will explain some ideas about the non-abelian case. All the results are joint with Oscar García-Prada.
Dienstag, den 16. Juli 2013 um 13:00 Uhr, in INF 288, HS 5 Dienstag, den 16. Juli 2013 at 13:00, in INF 288, HS 5
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Anna Wienhard