Illinois Journal of Mathematics

Higgs bundles over elliptic curves

Emilio Franco, Oscar Garcia-Prada, and 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.

Article information

Source
Illinois J. Math., Volume 58, Number 1 (2014), 43-96.

Dates
First available in Project Euclid: 1 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1427897168

Digital Object Identifier
doi:10.1215/ijm/1427897168

Mathematical Reviews number (MathSciNet)
MR3331841

Zentralblatt MATH identifier
06428021

Subjects
Primary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]

Citation

Franco, Emilio; Garcia-Prada, Oscar; Newstead, P. E. Higgs bundles over elliptic curves. Illinois J. Math. 58 (2014), no. 1, 43--96. doi:10.1215/ijm/1427897168. https://projecteuclid.org/euclid.ijm/1427897168


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