Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface

We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d (assumed coprime) on a Riemann surface of genus g greater than or equal to 2. We also use these formul...

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Bibliographic Details
Published inarXiv.org
Main Authors Jeffrey, Lisa C, Kirwan, Frances C
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 09.12.1997
Subjects
Bundles
Bundling
Homology
Mathematical analysis
Riemann surfaces
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Summary:We prove formulas (found by Witten in 1992 using physical methods) for intersection pairings in the cohomology of the moduli space M(n,d) of stable holomorphic vector bundles of rank n and degree d (assumed coprime) on a Riemann surface of genus g greater than or equal to 2. We also use these formulas for intersection numbers to obtain a proof of the Verlinde formula for the dimension of the space of holomorphic sections of a line bundle over M(n,d).
ISSN:2331-8422