{
  "id": "1009.4313",
  "version": "v2",
  "published": "2010-09-22T09:55:49.000Z",
  "updated": "2011-07-01T12:29:25.000Z",
  "title": "Fano 3-folds in codimension 4, Tom and Jerry, Part I",
  "authors": [
    "Gavin Brown",
    "Michael Kerber",
    "Miles Reid"
  ],
  "comment": "34pp. This article links to the Graded Ring Database http://grdb.lboro.ac.uk/, and more information is available from webloc. cit. + Downloads. Update includes several clarifications and improvements; results essentially unchanged. To appear in Comp. Math",
  "doi": "10.1112/S0010437X11007226",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "This work is part of the Graded Ring Database project [GRDB], and is a sequel to [Altinok's 1998 PhD thesis] and [Altinok, Brown and Reid, Fano 3-folds, K3 surfaces and graded rings, in SISTAG (Singapore, 2001), Contemp. Math. 314, 2002, pp. 25-53]. We introduce a strategy based on Kustin-Miller unprojection that constructs many hundreds of Gorenstein codimension 4 ideals with 9x16 resolutions (that is, 9 equations and 16 first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis. There are 115 cases whose numerical data (in effect, the Hilbert series) allow a Type I projection. In every case, at least one Tom and one Jerry construction works, providing at least two deformation families of quasismooth Fano 3-folds having the same numerics but different topology.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-01T12:29:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J45",
      "13D40",
      "14J28",
      "14J30",
      "14Q15"
    ],
    "keywords": [
      "codimension",
      "jerry construction works",
      "deformation families",
      "graded ring database project",
      "9x16 resolutions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4313B"
    }
  }
}