{
  "id": "0908.0289",
  "version": "v1",
  "published": "2009-08-03T16:07:55.000Z",
  "updated": "2009-08-03T16:07:55.000Z",
  "title": "A classification of terminal quartic 3-folds and applications to rationality questions",
  "authors": [
    "Anne-Sophie Kaloghiros"
  ],
  "comment": "40 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "This paper studies the birational geometry of terminal Gorenstein Fano 3-folds. If Y is not Q-factorial, in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, Weil non-Cartier divisors are generated by \"topological traces \" of K-negative extremal contractions on X. One can show, as an application of these methods, that a number of families of non-factorial terminal Gorenstein Fano 3-folds are rational. In particular, I give some examples of rational quartic hypersurfaces with Cl Y of rank 2, and show that when Cl Y has rank greater than 6, Y is always rational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-03T16:07:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30"
    ],
    "keywords": [
      "rationality questions",
      "terminal quartic",
      "application",
      "classification",
      "divisor class group cl"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.0289K"
    }
  }
}