{
  "id": "math/0402370",
  "version": "v1",
  "published": "2004-02-23T16:20:03.000Z",
  "updated": "2004-02-23T16:20:03.000Z",
  "title": "L. Szpiro's conjecture on Gorenstein algebras in codimension 2",
  "authors": [
    "Christian Böhning"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "A Gorenstein A-algebra R of codimension 2 is a perfect finite A-algebra such that R=Ext^2(R,A) holds as R-modules, A being a Cohen-Macaulay local ring with dim(A)-dim_A(R)=2. I prove a structure theorem for these algebras improving on an old theorem of M. Grassi. Special attention is paid to the question how the ring structure of R is encoded in its Hilbert resolution. It is shown that R is automatically a ring once one imposes a weak depth condition on a determinantal ideal derived from a presentation matrix of R over A. The interplay of Gorenstein algebras and Koszul modules as introduced by M. Grassi is clarified. Questions of applicability to canonical surfaces in P^4 have served as a guideline in these investigations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-23T16:20:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D02"
    ],
    "keywords": [
      "gorenstein algebras",
      "szpiros conjecture",
      "codimension",
      "perfect finite a-algebra",
      "weak depth condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2370B"
    }
  }
}