A Torelli theorem for moduli spaces of principal bundles over a curve

TL;DR

This paper proves that the isomorphism class of certain moduli spaces of principal bundles over a curve uniquely determines the underlying curve, extending Torelli-type results to nonabelian reductive groups.

Contribution

It establishes a Torelli theorem for moduli spaces of principal G-bundles over curves, showing the curve can be recovered from the moduli space.

Findings

Isomorphic moduli spaces imply isomorphic underlying curves

The result applies to nonabelian reductive complex groups

Provides a Torelli-type reconstruction for principal bundles

Abstract

Let X and X' be compact Riemann surfaces of genus at least 3, and let G and G' be nonabelian reductive complex groups. If one component M_G^d(X) of the moduli space for semistable principal G-bundles over X is isomorphic to another component M_{G'}^{d'}(X'), then X is isomorphic to X'.