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arXiv · 1004.1420

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

Mark Andrea de Cataldo·Tamas Hausel·Luca Migliorini
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Abstract

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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Mark Andrea de Cataldo, Tamas Hausel, Luca Migliorini. 2011-06-26. Topology of Hitchin systems and Hodge theory of character varieties: the case A_1. https://arxiv.org/abs/1004.1420

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