Vanishing of intersection numbers on the moduli space of Higgs bundles
Tamas Hausel
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 M 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 of M vanish, i.e. "there are no topological L2 harmonic forms on M". This result generalizes the well known vanishing of the Euler characteristic of the moduli space of rank 2 stable bundles N of fixed determinant of odd degree over ∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M) is given by relations analogous to the Mumford relations in the cohomology ring of N.
International Press
1998
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http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/1450
Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles. <i>Advances in Theoretical and Mathematical Physics</i>. 1998;2(5):1011-1040. doi:<a href="https://doi.org/10.4310/ATMP.1998.v2.n5.a3">10.4310/ATMP.1998.v2.n5.a3</a>
info:eu-repo/semantics/altIdentifier/doi/10.4310/ATMP.1998.v2.n5.a3
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