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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| Format: | Journal article |
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1996
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| author | Jeffrey, L Kirwan, F |
| author_facet | Jeffrey, L Kirwan, F |
| author_sort | Jeffrey, L |
| collection | OXFORD |
| description | 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). |
| first_indexed | 2024-03-07T00:20:17Z |
| format | Journal article |
| id | oxford-uuid:7c4d3cb8-79e6-4f5e-a6ae-7355f1ae3116 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:20:17Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:7c4d3cb8-79e6-4f5e-a6ae-7355f1ae31162022-03-26T20:56:09ZIntersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surfaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7c4d3cb8-79e6-4f5e-a6ae-7355f1ae3116Symplectic Elements at Oxford1996Jeffrey, LKirwan, FWe 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). |
| spellingShingle | Jeffrey, L Kirwan, F Intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a Riemann surface |
| title | Intersection theory on moduli spaces of holomorphic bundles of arbitrary
rank on a Riemann surface |
| title_full | Intersection theory on moduli spaces of holomorphic bundles of arbitrary
rank on a Riemann surface |
| title_fullStr | Intersection theory on moduli spaces of holomorphic bundles of arbitrary
rank on a Riemann surface |
| title_full_unstemmed | Intersection theory on moduli spaces of holomorphic bundles of arbitrary
rank on a Riemann surface |
| title_short | Intersection theory on moduli spaces of holomorphic bundles of arbitrary
rank on a Riemann surface |
| title_sort | intersection theory on moduli spaces of holomorphic bundles of arbitrary rank on a riemann surface |
| work_keys_str_mv | AT jeffreyl intersectiontheoryonmodulispacesofholomorphicbundlesofarbitraryrankonariemannsurface AT kirwanf intersectiontheoryonmodulispacesofholomorphicbundlesofarbitraryrankonariemannsurface |