Nonabelianization of Higgs bundles

Abstract

The character varieties of representations of a surface group into the Lie groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of the moduli space of Higgs bundles. We show that the fibres of the integrable system in these cases are not abelian varieties, but are instead moduli spaces of rank 2 bundles on a spectral curve, satisfying natural stability conditions.

References in corpus (1)

• Spectral data for U(m,m)-Higgs bundles

Cited by in corpus (10)

• Spectral data for U(m,m)-Higgs bundles
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• Cayley and Langlands type correspondences for orthogonal Higgs bundles
• Singular Geometry and Higgs Bundles in String Theory
• An introduction to spectral data for Higgs bundles
• Orthogonal Higgs bundles with singular spectral curves
• Higgs bundles, abelian gerbes and cameral data
• Higgs bundles and applications
• Hitchin Pairs for non-compact real Lie groups
• Topological invariants of parabolic $G$-Higgs bundles