{
  "id": "math/0702189",
  "version": "v1",
  "published": "2007-02-07T15:25:16.000Z",
  "updated": "2007-02-07T15:25:16.000Z",
  "title": "Enumerative geometry of Calabi-Yau 4-folds",
  "authors": [
    "A. Klemm",
    "R. Pandharipande"
  ],
  "comment": "44 pages",
  "journal": "Commun.Math.Phys.281:621-653,2008",
  "doi": "10.1007/s00220-008-0490-9",
  "categories": [
    "math.AG",
    "hep-th"
  ],
  "abstract": "Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in CP5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic anomaly equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-02-07T15:25:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "enumerative geometry",
      "gromov-witten theory",
      "moving multiple cover integrals",
      "sheaf theoretic explanation",
      "holomorphic anomaly equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 744180
    }
  }
}