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arXiv · 2603.21712

A universal Higgs bundle moduli space

Nigel Hitchin
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Abstract

We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichm\"uller space. The method uses a function f defined on the character variety, essentially the energy of a harmonic map, which is dependent on the complex structure of C. Using f we define a natural family of flat Ehresmann connections parametrized by the circle which reveal various aspects of these moduli spaces and their hyperk\"ahler metrics.

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Nigel Hitchin. 2026-03-23. A universal Higgs bundle moduli space. https://arxiv.org/abs/2603.21712

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