{
  "id": "math/9908054",
  "version": "v1",
  "published": "1999-08-12T01:54:55.000Z",
  "updated": "1999-08-12T01:54:55.000Z",
  "title": "Absolute and relative Gromov-Witten invariants of very ample hypersurfaces",
  "authors": [
    "Andreas Gathmann"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow groups of the moduli spaces of relative stable maps that relates these relative invariants to the Gromov-Witten invariants of X and Y. Given the Gromov-Witten invariants of X, we show that these relations are sufficient to compute all relative invariants, as well as all genus zero Gromov-Witten invariants of Y whose homology and cohomology classes are induced by X.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-08-12T01:54:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ample hypersurface",
      "genus zero relative gromov-witten invariants",
      "genus zero gromov-witten invariants",
      "smooth complex projective variety",
      "relative invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......8054G"
    }
  }
}