{
  "id": "math/9806133",
  "version": "v1",
  "published": "1998-06-23T20:42:41.000Z",
  "updated": "1998-06-23T20:42:41.000Z",
  "title": "Rational curves on hypersurfaces [after A. Givental]",
  "authors": [
    "Rahul Pandharipande"
  ],
  "comment": "33 pages, Latex2e",
  "categories": [
    "math.AG"
  ],
  "abstract": "This article accompanies my June 1998 seminaire Bourbaki talk on Givental's work. After a quick review of descendent integrals in Gromov-Witten theory, I discuss Givental's formalism relating hypergeometric series to solutions of quantum differential equations arising from hypersurfaces in projective space. A particular case of this relationship is a proof of the Mirror prediction for the numbers of rational curves on the Calabi-Yau quintic 3-fold. The approach taken here is entirely algebro-geometric and relies upon a localization formula on the moduli space of stable genus 0 maps to projective space. A different proof of the quintic Mirror prediction may be found in the work of Lian, Liu, and Yau.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-06-23T20:42:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational curves",
      "hypersurfaces",
      "giventals formalism relating hypergeometric series",
      "quintic mirror prediction",
      "seminaire bourbaki talk"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......6133P"
    }
  }
}