Finite group actions on moduli spaces of vector bundles

TL;DR

This paper investigates how finite groups act on moduli spaces of stable vector bundles and connects fixed points of these actions to representation varieties of orbifold fundamental groups.

Contribution

It introduces a novel relationship between group actions on moduli spaces and orbifold fundamental group representations.

Findings

Fixed points correspond to specific orbifold representations

Established a link between group actions and representation varieties

Provided new insights into the structure of moduli spaces

Abstract

We study actions of finite groups on moduli spaces of stable holomorphic vector bundles and relate the fixed-point sets of those actions to representation varieties of certain orbifold fundamental groups.