Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

Details Topology of Hitchin systems and Hodge theory of character varieties: the case A_1 Topology of Hitchin systems and Hodge theory of character varieties: the case A_1

2010-04-08

arxiv.org/abs/1004.1420v2

Mathematics

Algebraic Geometry

67 pages, arguments streamlined, to appear in Annals of Mathematics

Scientific paper

For G = GL_2, PGL_2 and SL_2 we prove that the perverse filtration associated to the Hitchin map on the cohomology of the moduli space of twisted G-Higgs bundles on a Riemann surface C agrees with the weight filtration on the cohomology of the twisted G character variety of C, when the cohomologies are identified via non-Abelian Hodge theory. The proof is accomplished by means of a study of the topology of the Hitchin map over the locus of integral spectral curves.

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