A conjectural description of the weight filtration of the
twisted character variety of a Riemann surface
Starts 23 Sep 2008 15:00
Ends 23 Sep 2008 20:00
Central European Time
Leonardo da Vinci Building Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
The variety parametrizing twisted representations with values in a reductive group G of the fundamental group of a Riemann surface has a natural structure of affine smooth variety, and, as such, has a mixed Hodge structure, recently investigated by Hausel and Rodriguez-Villegas.
By Hitchin theory, this variety is diffeomorphic to the moduli space of semistable principal bundles with a Higgs field.
This moduli space has a natural proper map, the Hitchin fibration, with target a linear space. We conjecture that the weight filtration of the cohomology of the character variety coincides with a filtration naturally associated to the topology of the Hitchin fibration.
We will discuss some evidence for this conjecture and a strategy.
Joint work with M. de Cataldo(SUNY) and T.Hausel(OXFORD)