{
  "id": "math/9904046",
  "version": "v1",
  "published": "1999-04-11T22:00:17.000Z",
  "updated": "1999-04-11T22:00:17.000Z",
  "title": "Quantization and ``theta functions''",
  "authors": [
    "Andrei Tyurin"
  ],
  "comment": "33 pp., to appear as Jussieu Math Preprint",
  "categories": [
    "math.AG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-04-11T22:00:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "theta functions",
      "geometric quantization links holomorphic geometry",
      "abelian variety",
      "complete linear system",
      "higher rank"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 498394,
      "adsabs": "1999math......4046T"
    }
  }
}