Vanishing of intersection numbers on the moduli space of Higgs bundles
In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface. We prove that all intersection numbers in the compact...
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| Format: | Journal article |
| Language: | English |
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1998
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| _version_ | 1797060100986241024 |
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| author | Hausel, T |
| author_facet | Hausel, T |
| author_sort | Hausel, T |
| collection | OXFORD |
| description | In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface. We prove that all intersection numbers in the compactly supported cohomology vanish, i.e. "there are no topological L^2 harmonic forms on Hitchin's space". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles of fixed determinant of odd degree over the given Riemann surface. Our proof shows that the vanishing of all intersection numbers in the compactly supported cohomology of Hitchin's space is given by relations analogous to Mumford's relations in the cohomology ring of the moduli space of stable bundles. |
| first_indexed | 2024-03-06T20:12:52Z |
| format | Journal article |
| id | oxford-uuid:2b2ba072-d7ae-44fa-86d1-e5b658c5c6c9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:12:52Z |
| publishDate | 1998 |
| record_format | dspace |
| spelling | oxford-uuid:2b2ba072-d7ae-44fa-86d1-e5b658c5c6c92022-03-26T12:29:21ZVanishing of intersection numbers on the moduli space of Higgs bundlesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2b2ba072-d7ae-44fa-86d1-e5b658c5c6c9EnglishSymplectic Elements at Oxford1998Hausel, TIn this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface. We prove that all intersection numbers in the compactly supported cohomology vanish, i.e. "there are no topological L^2 harmonic forms on Hitchin's space". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles of fixed determinant of odd degree over the given Riemann surface. Our proof shows that the vanishing of all intersection numbers in the compactly supported cohomology of Hitchin's space is given by relations analogous to Mumford's relations in the cohomology ring of the moduli space of stable bundles. |
| spellingShingle | Hausel, T Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title | Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title_full | Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title_fullStr | Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title_full_unstemmed | Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title_short | Vanishing of intersection numbers on the moduli space of Higgs bundles |
| title_sort | vanishing of intersection numbers on the moduli space of higgs bundles |
| work_keys_str_mv | AT hauselt vanishingofintersectionnumbersonthemodulispaceofhiggsbundles |