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Prym varieties of
spectral covers
Tamás Hausel and Christian Pauly |
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Geometry & Topology 16 (2012) 1609–1638
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Abstract |
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Given a possibly reducible and non-reduced spectral cover over a smooth projective complex curve we determine the group of connected components of the Prym variety . As an immediate application we show that the finite group of –torsion points of the Jacobian of acts trivially on the cohomology of the twisted –Higgs moduli space up to the degree which is predicted by topological mirror symmetry. In particular this yields a new proof of a result of Harder–Narasimhan, showing that this finite group acts trivially on the cohomology of the twisted stable bundle moduli space. |
Keywords
Prym varieties, Hitchin fibration, Higgs bundles, vector
bundles on curves
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Mathematical Subject Classification 2000
Primary: 14K30
Secondary: 14H60, 14H40
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References |
Publication
Received: 29 June 2011
Accepted: 8 June 2012
Published: 1 August 2012
Proposed: Frances Kirwan
Seconded: Jim Bryan, Richard Thomas
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Authors |
| Tamás Hausel | |
| Section de Mathématiques École Polytechnique Fédéral de Lausanne Section 8 CH-1015 Lausanne Switzerland |
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| http://geom.epfl.ch/Hausel | |
| Christian Pauly | |
| Laboratoire de Mathématiques J.A.
Dieudonné UMR no 7351 CNRS UNSA Université de Nice Sophia-Antipolis 06108 Nice Cedex 02 France |
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| http://math.unice.fr/~pauly/ | |
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