MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

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Funded by The Danish National Research Foundation

Geometric Mathematical Physics Seminar

Abstract
Let X be a compact Riemann surface of genus greater than or equal to 2. The semistable holomorphic vector bundles on X of rank n and determinant L are parametrised by the moduli space M(n,L). The Picard group of M(n,L) is isomorphic to Z with a unique ample generator K(n,L). The spaces Z_k(n,L) of holomorphic sections in the k'th tensor power of K(n,L) have been studied intensely, due to their central role in the gauge-theoretic approach to 2+1 dimensional TQFT. There is a natural action on M(n,L) of the group J^(n)(X) of n-torsion points in the Jacobian of X, gotten by tensoring with the corresponding line bundles. I define certain lifts of this action to K(n,L) (and hence to Z_k(n,L) and give a presentation of the group generated by such lifts. In the proces, a detailed study of the fixed point varieties for the action of J^(n)(X) on M(n,L) becomes necessary.

Contact person:Jørgen Ellegaard Andersen.