Topology of hitchin systems and Hodge theory of character varieties: The case A 1 Journal Article


Author(s): De Cataldo, Mark A; Hausel, Tamás; Migliorini, Luca
Article Title: Topology of hitchin systems and Hodge theory of character varieties: The case A 1
Affiliation
Abstract: For G = GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a compact Riemann surface C agrees with the weight filtration on the rational 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.
Keywords: character variety; compactified Jacobian; Hitchin fibration; perverse filtration; weight filtration
Journal Title: Annals of Mathematics
Volume: 175
Issue 3
ISSN: 0003-486X
Publisher: Princeton University Press  
Date Published: 2012-05-01
Start Page: 1329
End Page: 1407
URL:
DOI: 10.4007/annals.2012.175.3.7
Notes: Mark Andrea A. de Cataldo was partially supported by N.S.A. and N.S.F. Tamás Hausel was supported by a Royal Society University Research Fellowship. Luca Migliorini was partially supported by PRIN 2007 project "Spazi di moduli e teoria di Lie"
Open access: yes (repository)
IST Austria Authors
  1. Tamás Hausel
    31 Hausel
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