Higgs bundles over elliptic curves for complex reductive Lie groups

2013 
We study Higgs bundles over an elliptic curve with connected complex reductive structure group, describing their moduli spaces and the associated Hitchin fibration; it follows from our description that these spaces are irreducible and normal. We also describe the other spaces involved in non-abelian Hodge theory, namely the moduli spaces of bundles with projectively flat connections and representations of surface groups.
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