Higgs bundles over elliptic curves for real groups

TL;DR

This paper investigates the structure and moduli space of topologically trivial G-Higgs bundles over elliptic curves for real groups, providing a detailed description of their Hitchin fibration and related morphisms.

Contribution

It offers a comprehensive description of the moduli space and Hitchin fibration for G-Higgs bundles over elliptic curves when G is a real form of a complex semisimple Lie group.

Findings

Description of the reduced moduli space

Analysis of the Hitchin fibration

Finite morphism to complex Higgs bundle moduli space

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 $G^{\mathbb{C}}$. We achieve a description of their (reduced) moduli space, the associated Hitchin fibration and the finite morphism to the moduli space of $G^{\mathbb{C}}$-Higgs bundles.