For G = GL2, PGL2, SL2 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.
Topology of Hitchin systems and Hodge theory of character varieties: the case A1 / M.A. de Cataldo; T. Hausel; L. Migliorini. - In: ANNALS OF MATHEMATICS. - ISSN 0003-486X. - STAMPA. - 175:(2012), pp. 1329-1407. [10.4007/annals.2012.175.3.7]
Topology of Hitchin systems and Hodge theory of character varieties: the case A1
MIGLIORINI, LUCA
2012
Abstract
For G = GL2, PGL2, SL2 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.