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

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...

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Bibliographic Details
Main Authors Jeffrey, Lisa C, Kiem, Young-Hoon, Kirwan, Frances C, Woolf, Jonathan
Format Journal Article
LanguageEnglish
Published 17.05.2005
Subjects
Mathematics - Algebraic Geometry
Mathematics - Symplectic Geometry
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Summary: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.
DOI:10.48550/arxiv.math/0505362