Automorphisms of moduli spaces of principal bundles over a smooth curve

TL;DR

This paper characterizes the automorphism group of the moduli space of semistable principal G-bundles over a smooth curve, using Hitchin fibration analysis, and describes key singular loci in the Hitchin base.

Contribution

It provides a detailed description of automorphisms of moduli spaces for almost-simple groups and analyzes singular fibers of the Hitchin fibration in characteristic zero.

Findings

Automorphism group of the moduli space is explicitly described.

Irreducible components of singular cameral curves are characterized.

Structure of singular Hitchin fibers is elucidated.

Abstract

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least $4$. The result is achieved by studying the singular fibers of the Hitchin fibration. As a byproduct, we provide a description of the irreducible components of two natural closed subsets in the Hitchin basis: the divisor of singular cameral curves and the divisor of singular Hitchin fibers.