Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations

2005/05/17 by Lisa C. Jeffrey, Young‐Hoon Kiem, Jeffrey, Lisa C. +5 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0505362

Abstract

This paper studies intersection theory on the compactified moduli space M(n,d) of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface of genus g > 1 where n and d may have common factors. Because of the presence of singularities we work with the intersection cohomology groups defined by Goresky and MacPherson and the ordinary cohomology groups of a certain partial resolution of singularities of M(n,d). Based on our earlier work, we give a precise formula for the intersection cohomology pairing and provide a method to calculate pairings on the partial resolution of singularities of M(n,d). The case when n=2 is discussed in detail. Finally Witten's integral is considered for this singular case.

Cited by

• Generalized intersection pairings on moduli spaces of vector bundles over a curve

Related

• Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface
• Intersection cohomology of representation spaces of surface groups
• Intersection cohomology of moduli spaces of vector bundles over curves
• Parabolic bundles and the intersection cohomology of moduli spaces of vector bundles on curves
• On the intersection theory of the moduli space of rank two bundles