Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A universal Higgs bundle moduli space

Nigel Hitchin

Abstract

We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichmüller 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 hyperkähler metrics.

A universal Higgs bundle moduli space

Abstract

We give a differential geometric construction of the holomorphic family of Higgs bundle moduli spaces over a curve C as a fibration over Teichmüller 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 hyperkähler metrics.
Paper Structure (15 sections, 2 theorems, 39 equations)

This paper contains 15 sections, 2 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. The function $f$
  3. Basic properties
  4. Variation of $f$
  5. Variation of the hyperkähler metric
  6. The symplectic connection
  7. Applications
  8. Holonomy
  9. The Levi form
  10. ${\mathcal{M}}\times \mathcal{T}$ as a complex manifold
  11. An example
  12. Further aspects
  13. Real forms
  14. The prequantum line bundle
  15. Semiflat metrics

Key Result

Proposition 1

$\dot\omega_2$ is of type $(1,1)$ with respect to all complex structures.

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2