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arXiv · 1801.09666

Involutions of rank 2 Higgs bundle moduli spaces

Oscar Garcia-Prada·S. Ramanan
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Abstract

We consider the moduli space of rank 2 Higgs bundles with fixed determinant over a smooth projective curve X of genus 2 over the complex numbers, and study involutions defined by tensoring the vector bundle with an element $\alpha$ of order 2 in the Jacobian of the curve, combined with multiplication of the Higgs field by $\pm 1$. We describe the fixed points of these involutions in terms of the Prym variety of the covering of $X$ defined by $\alpha$, and give an interpretation in terms of the moduli space of representations of the fundamental group.

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Oscar Garcia-Prada, S. Ramanan. 2018-01-29. Involutions of rank 2 Higgs bundle moduli spaces. https://arxiv.org/abs/1801.09666

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