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

M. De Cataldo, T. Hausel, L. Migliorini, Annals of Mathematics 175 (2012) 1329–1407.


Journal Article | Published
Author
De Cataldo, Mark A; Hausel, TamasIST Austria; Migliorini, Luca
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.
Publishing Year
Date Published
2012-05-01
Journal Title
Annals of Mathematics
Acknowledgement
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"
Volume
175
Issue
3
Page
1329 - 1407
IST-REx-ID

Cite this

De Cataldo M, Hausel T, Migliorini L. Topology of hitchin systems and Hodge theory of character varieties: The case A 1. Annals of Mathematics. 2012;175(3):1329-1407. doi:10.4007/annals.2012.175.3.7
De Cataldo, M., Hausel, T., & Migliorini, L. (2012). Topology of hitchin systems and Hodge theory of character varieties: The case A 1. Annals of Mathematics, 175(3), 1329–1407. https://doi.org/10.4007/annals.2012.175.3.7
De Cataldo, Mark, Tamas Hausel, and Luca Migliorini. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” Annals of Mathematics 175, no. 3 (2012): 1329–1407. https://doi.org/10.4007/annals.2012.175.3.7.
M. De Cataldo, T. Hausel, and L. Migliorini, “Topology of hitchin systems and Hodge theory of character varieties: The case A 1,” Annals of Mathematics, vol. 175, no. 3, pp. 1329–1407, 2012.
De Cataldo M, Hausel T, Migliorini L. 2012. Topology of hitchin systems and Hodge theory of character varieties: The case A 1. Annals of Mathematics. 175(3), 1329–1407.
De Cataldo, Mark, et al. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” Annals of Mathematics, vol. 175, no. 3, Princeton University Press, 2012, pp. 1329–407, doi:10.4007/annals.2012.175.3.7.
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