# Sectional curvature asymptotics of the Higgs bundle moduli space

## TL;DR

This paper analyzes the asymptotic behavior of sectional curvatures in the Higgs bundle moduli space with respect to large Higgs fields, revealing explicit Dirac-type contributions on the surface.

## Contribution

It provides the first detailed asymptotic analysis of the sectional curvatures of the $L^2$ hyperk"ahler metric on rank-2 Higgs bundle moduli spaces, including explicit formulas.

## Key findings

- Sectional curvatures exhibit Dirac-type asymptotics on the surface.
- Leading order behavior is explicitly characterized.
- Results hold away from the discriminant locus.

## Abstract

We determine the asymptotic behavior in the limit of large Higgs fields of the sectional curvatures of the natural $L^2$ hyperk\"ahler metric $G_{L^2}$ of the moduli space $\mathcal M$ of rank-$2$ Higgs bundles on a Riemann surface $\Sigma$ away from the discriminant locus. It is shown that their leading order part is given by a sum of Dirac type contributions on $\Sigma$, for which we find explicit expressions.