Higgs bundles over elliptic curves for real groups

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 . We achieve a description of their (reduced) moduli space, the associated Hitchin fibration and the finite morphism to the moduli space of G -Higgs bundles.The first author was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo through FAPESP 2012/16356-6 and BEPE-2015/06696-2. The second author was partially supported by the Ministerio de Economiá y Competitividad of Spain through Project MTM2010-17717 and Severo Ochoa Excellence Grant