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 $L^2$ hyperkähler 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.

Some typos corrected, improved exposition

References in corpus (1)

• Asymptotic behaviour of certain families of harmonic bundles on Riemann surfaces