Higgs bundles over elliptic curves for real groups

2016/05/14 by Emilio Franco, Franco, Emilio, Oscar Garcı́a-Prada +3 · 1 citation
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.1605.04409

openalex publication_date 2016/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study topologically trivial G-Higgs bundles over an elliptic curve X when the structure group G is a connected real form of a complex semisimple Lie group G^ℂ. We achieve a description of their (reduced) moduli space, the associated Hitchin fibration and the finite morphism to the moduli space of G^ℂ-Higgs bundles.

Citations

• The Self-Duality Equations on a Riemann Surface

Cited by

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

Related

• Higgs bundles over elliptic curves for complex reductive Lie groups
• Involutions of the moduli spaces of G-Higgs bundles over elliptic curves
• Real Higgs pairs and Non-abelian Hodge correspondence on a Klein surface
• The Hitchin morphism for certain surfaces fibered over a curve
• Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group