A universal Higgs bundle moduli space
Differential Geometry
2026-03-24 v1
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.
Keywords
Cite
@article{arxiv.2603.21712,
title = {A universal Higgs bundle moduli space},
author = {Nigel Hitchin},
journal= {arXiv preprint arXiv:2603.21712},
year = {2026}
}