Geometry & Topology
- Geom. Topol.
- Volume 16, Number 3 (2012), 1609-1638.
Prym varieties of spectral covers
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.
Geom. Topol., Volume 16, Number 3 (2012), 1609-1638.
Received: 29 June 2011
Accepted: 8 June 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14K30: Picard schemes, higher Jacobians [See also 14H40, 32G20]
Secondary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05] 14H40: Jacobians, Prym varieties [See also 32G20]
Hausel, Tamás; Pauly, Christian. Prym varieties of spectral covers. Geom. Topol. 16 (2012), no. 3, 1609--1638. doi:10.2140/gt.2012.16.1609. https://projecteuclid.org/euclid.gt/1513732444