Volume 16, issue 3 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Prym varieties of spectral covers

Tamás Hausel and Christian Pauly

Geometry & Topology 16 (2012) 1609–1638
Abstract

Given a possibly reducible and non-reduced spectral cover π: X C over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(XC). As an immediate application we show that the finite group of n–torsion points of the Jacobian of C acts trivially on the cohomology of the twisted SLn–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 SLn stable bundle moduli space.

Keywords
Prym varieties, Hitchin fibration, Higgs bundles, vector bundles on curves
Mathematical Subject Classification 2000
Primary: 14K30
Secondary: 14H60, 14H40
References
Publication
Received: 29 June 2011
Accepted: 8 June 2012
Published: 1 August 2012
Proposed: Frances Kirwan
Seconded: Jim Bryan, Richard Thomas
Authors
Tamás Hausel
Section de Mathématiques
École Polytechnique Fédéral de Lausanne
Section 8
CH-1015 Lausanne
Switzerland
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
http://math.unice.fr/~pauly/