Prym varieties of spectral covers

Details Prym varieties of spectral covers Prym varieties of spectral covers

2010-12-21

arxiv.org/abs/1012.4748v2

Mathematics

Algebraic Geometry

22 pages, applications to topological mirror symmetry and a result of Harder--Narasimhan are added

Scientific paper

Given a possibly reducible and non-reduced spectral cover X over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). 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 SL_n-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 SL_n stable bundle moduli space.

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