Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case

TL;DR

This paper investigates the geometry of Higgs bundle moduli spaces with non-zero degree, introducing semi-flat metrics and comparing their asymptotic behavior with Hitchin metrics along specific deformations.

Contribution

It defines a semi-flat metric for non-zero degree Higgs bundles and analyzes its asymptotic relation to the Hitchin metric along certain rays.

Findings

Semi-flat metric introduced for non-zero degree Higgs bundles.

Asymptotic comparison between semi-flat and Hitchin metrics conducted.

Results enhance understanding of metric behavior in Higgs bundle moduli spaces.

Abstract

We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero degree case, we introduce the semi-flat metric, and compare the asymptotic behaviour of the semi-flat metric and the Hitchin metric along the ray $(E,t\theta)$ $(t\to\infty)$.