{
  "id": "1106.3890",
  "version": "v2",
  "published": "2011-06-20T13:16:18.000Z",
  "updated": "2016-12-29T16:45:41.000Z",
  "title": "Bundles of generalized theta functions over abelian surfaces",
  "authors": [
    "Dragos Oprea"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drezet-Narasimhan from curves to abelian surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-20T13:16:18.000Z",
      "abstract": "We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. The splitting type of these bundles is conjecturally expressed in terms of a new class of semihomogeneous bundles. The conjecture is confirmed in degree zero. Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. A version of level 1 strange duality is established.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-12-29T16:45:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian surfaces",
      "strange duality",
      "moduli spaces",
      "fourier-mukai symmetries",
      "verlinde bundles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3890O"
    }
  }
}