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Some cohomology calculations of moduli spaces of Higgs bundles and related spaces

Jochen Heinloth
(University of Amsterdam)
Wednesday, 12 May, 2010, at 16:15-17:15, in Aud. D3 (1531-215)
Most of the talk is a report on a joint work with L. Alvarez-Consul, M. Logares and O. Garcia-Prada and A. Schmitt. When Hitchin introduced the moduli space of Higgs-bundles he also gave a strategy to compute the cohomology of the moduli space of Higgs-bundles, using the $C^*$ action on the moduli space. This strategy has only been completed in very few cases. We would like to explain our approach to this strategy. Our approach differs from previous computations in two respects. First, our computations are done in the Grothendieck ring of varieties. Also we replace arguments using a variation of stability parameters by computations for the underlying algebraic stacks, without stability conditions. In the cases that were previously known, this seems to shorten the computations and allows us to do some new computations.
Organised by: CTQM/QGM
Contact person: Jørgen Ellegaard Andersen