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

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.


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. Princeton University Press. https://doi.org/10.4007/annals.2012.175.3.7
De Cataldo, Mark, Tamás Hausel, and Luca Migliorini. “Topology of Hitchin Systems and Hodge Theory of Character Varieties: The Case A 1.” Annals of Mathematics. Princeton University Press, 2012. 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. Princeton University Press, 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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