Chen-Ruan cohomology of some moduli spaces, II

TL;DR

This paper computes the Chen-Ruan cohomology of a specific orbifold formed by the moduli space of stable vector bundles over a Riemann surface, considering the action of a certain line bundle group.

Contribution

It provides the first detailed computation of Chen-Ruan cohomology for these moduli spaces under the action of the line bundle group.

Findings

Explicit Chen-Ruan cohomology groups computed

Description of orbifold structure of moduli space

Insights into the topology of moduli spaces under group actions

Abstract

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable vector bundles over X of rank r and determinant \xi. By \Gamma we will denote the group of line bundles L over X such that $L^{\otimes r}$ is trivial. This group \Gamma acts on {\mathcal M}_\xi(r). We compute the Chen-Ruan cohomology of the corresponding orbifold.