Geometry & Topology

Prym varieties of spectral covers

Tamás Hausel and Christian Pauly

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Given a possibly reducible and non-reduced spectral cover π:XC 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.

Article information

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

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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]

Prym varieties Hitchin fibration Higgs bundles vector bundles on curves


Hausel, Tamás; Pauly, Christian. Prym varieties of spectral covers. Geom. Topol. 16 (2012), no. 3, 1609--1638. doi:10.2140/gt.2012.16.1609.

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