The Hodge theory of character varieties

Details The Hodge theory of character varieties The Hodge theory of character varieties

2010-11-03

arxiv.org/abs/1011.0784v1

Mathematics

Algebraic Geometry

To appear in the proceedings of the conference "Classical algebraic geometry today, M.S.R.I., Berkeley, January 25-29, 2009."

Scientific paper

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.

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