Chen–Ruan cohomology of some moduli spaces of parabolic vector bundles

Abstract

Let ( X , D ) be an ℓ-pointed compact Riemann surface of genus at least two. For each point x ∈ D , fix parabolic weights ( α 1 ( x ) , α 2 ( x ) ) such that ∑ x ∈ D ( α 1 ( x ) − α 2 ( x ) ) < 1 / 2 . Fix a holomorphic line bundle ξ over X of degree one. Let P M ξ denote the moduli space of stable parabolic vector bundles, of rank two and determinant ξ, with parabolic structure over D and parabolic weights { ( α 1 ( x ) , α 2 ( x ) ) } x ∈ D . The group of order two line bundles over X acts on P M ξ by the rule E ∗ ⊗ L ↦ E ∗ ⊗ L . We compute the Chen–Ruan cohomology ring of the corresponding orbifold.