{
  "id": "math/0507104",
  "version": "v1",
  "published": "2005-07-05T18:57:21.000Z",
  "updated": "2005-07-05T18:57:21.000Z",
  "title": "On the Genus-One Gromov-Witten Invariants of Complete Intersections",
  "authors": [
    "Jun Li",
    "Aleksey Zinger"
  ],
  "comment": "45 pages, 4 figures, 1 table",
  "categories": [
    "math.AG",
    "math.SG"
  ],
  "abstract": "As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component $\\ov\\M_{1,k}^0(\\P,d)$ of the moduli space of stable genus-one holomorphic maps into $\\P$ have a well-defined euler class. In this paper, we extend this result to moduli spaces of perturbed, in a restricted way, $J$-holomorphic maps. We show that euler classes of such cones relate the reduced genus-one Gromov-Witten invariants of complete intersections to the corresponding GW-invariants of the ambient projective space. As a consequence, the standard genus-one GW-invariants of complete intersections can be expressed in terms of the genus-zero and genus-one GW-invariants of projective spaces. We state such a relationship explicitly for complete-intersection threefolds. A relationship for higher-genus invariants is conjectured as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-05T18:57:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "53D45"
    ],
    "keywords": [
      "complete intersections",
      "moduli space",
      "holomorphic vector bundle sections",
      "projective space",
      "reduced genus-one gromov-witten invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7104L"
    }
  }
}