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2016•Unpublished venueRequires access

Prym varieties of spectral covers

Christian Pauly

Open publisher page 22 citations

Abstract

Given a possibly reducible and non-reduced spectral cover W 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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What this paper is about

Given a possibly reducible and non-reduced spectral cover W 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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Available abstract

Given a possibly reducible and non-reduced spectral cover W 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.

Key concepts: Mathematics, Moduli space, Pure mathematics, Spectral sequence, Cohomology, Torsion (gastropod), Mirror symmetry, Group (periodic table)

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