{
  "id": "1304.5248",
  "version": "v1",
  "published": "2013-04-18T20:33:51.000Z",
  "updated": "2013-04-18T20:33:51.000Z",
  "title": "Gorenstein in codimension 4 - the general structure theory",
  "authors": [
    "Miles Reid"
  ],
  "comment": "To appear in Algebraic Geometry in East Asia (Taipei Nov 2011), Advanced Studies in Pure Mathematics, 2013. 30 pp, The website http://www.warwick.ac.uk/staff/Miles.Reid/codim4 contains material accompanying this paper",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "I describe the projective resolution of a codimension 4 Gorenstein ideal, aiming to extend Buchsbaum and Eisenbud's famous result in codimension 3. The main result is a structure theorem stating that the ideal is determined by its (k+1) x 2k matrix of first syzygies, viewed as a morphism from the ambient regular space to the Spin-Hom variety SpH_k in Mat(k+1,2k). This is a general result encapsulating some theoretical aspects of the problem, but, as it stands, is still some way from tractable applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-18T20:33:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13H10",
      "13D25",
      "13D02",
      "14J10",
      "14M05"
    ],
    "keywords": [
      "general structure theory",
      "codimension",
      "ambient regular space",
      "first syzygies",
      "eisenbuds famous result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5248R"
    }
  }
}