{
  "id": "0903.1335",
  "version": "v2",
  "published": "2009-03-07T10:41:36.000Z",
  "updated": "2010-01-27T14:18:26.000Z",
  "title": "Parallel Kustin--Miller unprojection with an application to Calabi--Yau geometry",
  "authors": [
    "Jorge Neves",
    "Stavros Argyrios Papadakis"
  ],
  "comment": "25 pages. v2: Applications in Section 4 expanded",
  "doi": "10.1112/plms/pds036",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Kustin--Miller unprojection constructs more complicated Gorenstein rings from simpler ones. Geometrically, it inverts certain projections, and appears in the constructions of explicit birational geometry. However, it is often desirable to perform not only one but a series of unprojections. The main aim of the present paper is to develop a theory, which we call parallel Kustin--Miller unprojection, that applies when all the unprojection ideals of a series of unprojections correspond to ideals already present in the initial ring. As an application of the theory, we explicitly construct 7 families of Calabi--Yau 3-folds of high codimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-27T14:18:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M05",
      "14J32",
      "13H10",
      "14E99"
    ],
    "keywords": [
      "parallel kustin-miller unprojection",
      "calabi-yau geometry",
      "application",
      "kustin-miller unprojection constructs",
      "explicit birational geometry"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.1335N"
    }
  }
}