Involutions of the moduli spaces of G-Higgs bundles over elliptic curves

2016/12/26 by Indranil Biswas, Biswas, Indranil, Luis Ángel Calvo Pascual +5
Mathematics · #14D20 #14H52 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1612.08364

openalex publication_date 2016/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a systematic study of involutions on the moduli space of G-Higgs bundles over an elliptic curve X, where G is complex reductive affine algebraic group. The fixed point loci in the moduli space of G-Higgs bundles on X, and in the moduli space of representations of the fundamental group of X into G, are described. This leads to an explicit description of the moduli spaces of pseudo-real G-Higgs bundles over X.

Citations

• The Self-Duality Equations on a Riemann Surface
• Higgs bundles over elliptic curves for real groups

Related

• Higgs bundles over elliptic curves for real groups
• Higgs bundles over elliptic curves for complex reductive Lie groups
• Involutions of rank 2 Higgs bundle moduli spaces
• Anti-holomorphic involutions of the moduli spaces of Higgs bundles
• Moduli spaces of parabolic U(p,q)-Higgs bundles