Hodge structure on the cohomology of the moduli space of Higgs bundles

2001/12/12 by Mridul Mehta, Mehta, Mridul
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.math/0112111

7 pages. The only change is the addition of a reference to the proof of the generation theorem for general rank by E. Markman

openalex publication_date 2001/12/12 · arxiv created 2002/11/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In this paper, we use their results to compute the Hodge structure on the cohomology of this moduli space. We show that the natural Hodge structure on H^k is pure of weight k.

Citations

• The Self-Duality Equations on a Riemann Surface

Related

• Relations in the cohomology ring of the moduli space of rank 2 Higgs bundles
• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• Geometry of the moduli space of Higgs bundles
• Cohomology of the moduli of Higgs bundles via positive characteristic
• Variations of Hodge Structures of Rank Three k-Higgs Bundles and Moduli\n Spaces of Holomorphic Triples