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

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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.
51 pages; 1 figure

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Algebraic Geometry, Symplectic Geometry, 53D99

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http://salesiana.dossiersoluciones.com/handle/123456789/101281

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505362
 http://arxiv.org/abs/math/0505362

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arXiv