Prym varieties of spectral covers
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(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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3
1609 - 1638
1609 - 1638
University of Warwick