{
  "id": "0901.0690",
  "version": "v3",
  "published": "2009-01-06T18:42:40.000Z",
  "updated": "2009-04-27T07:01:58.000Z",
  "title": "Castelnuovo-Mumford regularity of deficiency modules",
  "authors": [
    "Markus Brodmann",
    "Maryam Jahangiri",
    "Cao Huy Linh"
  ],
  "comment": "25 pages, the previous version divided in two parts",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "Let $d \\in \\N$ and let $M$ be a finitely generated graded module of dimension $\\leq d$ over a Noetherian homogeneous ring $R$ with local Artinian base ring $R_0$. Let $\\beg(M)$, $\\gendeg(M)$ and $\\reg(M)$ respectively denote the beginning, the generating degree and the Castelnuovo-Mumford regularity of $M$. If $i \\in \\N_0$ and $n \\in Z$, let $d^i_M(n)$ denote the $R_0$-length of the $n$-th graded component of the $i$-th $R_+$-transform module $D^i_{R_+}(M)$ of $M$ and let $K^i(M)$ denote the $i$-th deficiency module of $M$. Our main result says, that $\\reg(K^i(M))$ is bounded in terms of $\\beg(M)$ and the \"diagonal values\" $d^j_M(-j)$ with $j = 0,..., d-1$. As an application of this we get a number of further bounding results for $\\reg(K^i(M))$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-04-27T07:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D45",
      "13D40"
    ],
    "keywords": [
      "castelnuovo-mumford regularity",
      "th deficiency module",
      "main result says",
      "th graded component",
      "transform module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}