{
  "id": "math/0403300",
  "version": "v2",
  "published": "2004-03-18T10:31:56.000Z",
  "updated": "2004-03-23T15:51:14.000Z",
  "title": "On the Quantum Cohomology of some Fano threefolds and a conjecture of Dubrovin",
  "authors": [
    "Gianni Ciolli"
  ],
  "comment": "15 pages, 3 tables. In v2 two small mistakes were corrected: a missing hypothesis in the citation of Theorem 6 and a wrong bibliographic citation",
  "categories": [
    "math.AG"
  ],
  "abstract": "In the present paper the small Quantum Cohomology ring of some Fano threefolds which are obtained as one- or two-curve blow-ups from $P^3$ or the quadric $Q^3$ is explicitely computed. Because of systematic usage of the associativity property of quantum product only a very small and enumerative subset of Gromov-Witten invariants is needed. Then, for these threefolds the Dubrovin conjecture on the semisimplicity of Quantum Cohomology is proven by checking the computed Quantum Cohomology rings and by showing that a smooth Fano threefold $X$ with $b_3(X)=0$ admits a complete exceptional set of the appropriate length.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-23T15:51:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14J45"
    ],
    "keywords": [
      "smooth fano threefold",
      "complete exceptional set",
      "systematic usage",
      "quantum product",
      "appropriate length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3300C"
    }
  }
}