A universal Higgs bundle moduli space
Nigel Hitchin

TL;DR
This paper constructs a holomorphic family of Higgs bundle moduli spaces over a curve using differential geometry, linking harmonic map energy to complex structures and revealing hyperk"ahler metric properties.
Contribution
It introduces a novel differential geometric approach to parametrize Higgs bundle moduli spaces over Teichm"uller space via a harmonic map energy function.
Findings
Construction of a holomorphic family over Teichm"uller space
Definition of flat Ehresmann connections parametrized by the circle
Insights into hyperk"ahler metrics of the moduli spaces
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Analytic and geometric function theory
