Topology of Hitchin systems and Hodge theory of character varieties: the case A1

• 成果类型: Article
• 署名作者: de Cataldo, Mark Andrea A.; Hausel, Tamas; Migliorini, Luca
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.175.3.7
• 发表日期: 2012
• 页码: 1329-1407
• 关键词: lefschetz hyperplane theorem; self-duality equations; rank-2 higgs bundles; moduli space; decomposition theorem; riemann surface; cohomology ring; stable bundles; algebraic maps; CURVES

摘要

For G = GL(2), PGL(2), 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.