Vector bundles on curves and generalized theta functions: recent results and open problems

Details Vector bundles on curves and generalized theta functions: recent results and open problems Vector bundles on curves and generalized theta functions: recent results and open problems

1994-04-05

arxiv.org/abs/alg-geom/9404001v1

Mathematics

Algebraic Geometry

15 pages, Plain TeX

Scientific paper

Riemann surface carries a natural line bundle, the determinant bundle. The space of sections of this line bundle (or its multiples) constitutes a natural non-abelian generalization of the spaces of theta functions on the Jacobian. There has been much progress in the last few years towards a better understanding of these spaces, including a rigorous proof of the celebrated Verlinde formula which gives their dimension. This survey paper tries to explain what is now known and what remains open.

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