Chen–Ruan cohomology and moduli spaces of parabolic bundles over a Riemann surface

Abstract

Let \((X,\,D)\) be an m-pointed compact Riemann surface of genus at least 2. For each \(x \,\in \, D\), fix full flag and concentrated weight system \(\alpha \). Let \(P \mathcal {M}_{\xi }\) denote the moduli space of semi-stable parabolic vector bundles of rank r and determinant \(\xi \) over X with weight system \(\alpha \), where r is a prime number and \(\xi \) is a holomorphic line bundle over X of degree d which is not a multiple of r. We compute the Chen–Ruan cohomology of the orbifold for the action on \(P \mathcal {M}_{\xi }\) of the group of r-torsion points in \(\mathrm{Pic}^0(X)\).