Sectional curvature asymptotics of the Higgs bundle moduli space

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.