Hitchin fibrations are Ng\^{o} fibrations

TL;DR

This paper demonstrates that Hitchin fibrations for G-Higgs bundles over a curve can be viewed as Ngô fibrations, establishing their structure as weak Abelian fibrations and analyzing their cohomological properties.

Contribution

It proves that Hitchin fibrations are weak Abelian fibrations and establishes cohomological bounds and regularity in specific cases.

Findings

Hitchin fibrations admit the structure of weak Abelian fibrations.

Cohomological bounds are established for certain line bundle twists.

The fibrations exhibit δ-regularity under specific conditions.

Abstract

We study the geometry of the Hitchin fibration for $\mathcal{L}$-valued $G$-Higgs bundles over a smooth projective curve of genus $g$, where $G$ is a reductive group and $\mathcal{L}$ is a suitably positive line bundle. We show that the Hitchin fibration admits the structure of a weak Abelian fibration. In the case when the line bundle $\mathcal{L}$ is a twist of the canonical bundle of the curve by a (possibly empty) reduced effective divisor, we prove a cohomological bound and $\delta$-regularity of the weak Abelian fibration.