The Hodge theory of character varieties
Algebraic Geometry
2010-11-04 v1
Abstract
This is a report on joint work with T. Hausel and L. Migliorini, where we prove, for each of the groups GL(2,C), PGL(2,C), SL(2,C), that the non-Abelian Hodge theorem identifies the weight filtration on the cohomology of the character variety with the perverse Leray filtration on the cohomology of the domain of the Hitchin map. We review the decomposition theorem, N\^go's support theorem, the geometric description of the perverse filtration and the sub-additivity of the Leray filtration with respect to the cup product.
Keywords
Cite
@article{arxiv.1011.0784,
title = {The Hodge theory of character varieties},
author = {Mark Andrea de Cataldo},
journal= {arXiv preprint arXiv:1011.0784},
year = {2010}
}
Comments
To appear in the proceedings of the conference "Classical algebraic geometry today, M.S.R.I., Berkeley, January 25-29, 2009." Expanded version of my talk