Higgs bundles over elliptic curves

Emilio Franco; Oscar Garcia-Prada; P. E. Newstead

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arXiv · 1302.2881

Higgs bundles over elliptic curves

Emilio Franco·Oscar Garcia-Prada·P. E. Newstead

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Abstract

In this paper we study $G$-Higgs bundles over an elliptic curve when the structure group $G$ is a classical complex reductive Lie group. Modifying the notion of family, we define a new moduli problem for the classification of semistable $G$-Higgs bundles of a given topological type over an elliptic curve and we give an explicit description of the associated moduli space as a finite quotient of a product of copies of the cotangent bundle of the elliptic curve. We construct a bijective morphism from this new moduli space to the usual moduli space of semistable $G$-Higgs bundles, proving that the former is the normalization of the latter. We also obtain an explicit description of the Hitchin fibration for our (new) moduli space of $G$-Higgs bundles and we study the generic and non-generic fibres.

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BibTeX RIS

Emilio Franco, Oscar Garcia-Prada, P. E. Newstead. 2013-02-12. Higgs bundles over elliptic curves. https://arxiv.org/abs/1302.2881

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