Quantization and ``theta functions''

Details Quantization and ``theta functions'' Quantization and ``theta functions''

1999-04-11

arxiv.org/abs/math/9904046v1

Mathematics

Algebraic Geometry

33 pp., to appear as Jussieu Math Preprint

Scientific paper

Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how to use this treatment to construct a special basis in every space of conformal blocks. This is a direct generalization of the basis of theta functions with characteristics in every complete linear system on an Abelian variety (see Mumford's "Tata lectures on theta" cite(Mumford)). The same construction generalizes the classical theory of theta functions to vector bundles of higher rank on Abelian varieties and K3 surfaces. We also discuss the geometry behind these constructions.

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