The Hitchin morphism for K-trivial varieties

TL;DR

This paper investigates the Hitchin morphism for higher-dimensional K-trivial varieties, demonstrating that for a specific class called r-small, the spectral base matches the image of the moduli space, confirming a conjecture in this context.

Contribution

It proves a stronger version of Chen and Ngô's conjecture for r-small varieties, including K-trivial varieties, by analyzing the spectral covers and their normality.

Findings

The set-theoretic image of the Hitchin morphism equals the spectral base for r-small varieties.

A modified construction of spectral covers yields normal spectral covers.

The result confirms the conjecture for a class of higher-dimensional varieties.

Abstract

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the spectral base. In other words, a stronger version of the conjecture of Chen and Ng\^o holds for this class of varieties, which includes K-trivial varieties. As part of the proof, we slightly modify the construction of spectral covers to obtain normal spectral covers.