{
  "id": "math/0510395",
  "version": "v1",
  "published": "2005-10-18T21:40:49.000Z",
  "updated": "2005-10-18T21:40:49.000Z",
  "title": "Bounds on the Castelnuovo-Mumford regularity of tensor products",
  "authors": [
    "Giulio Caviglia"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AC",
    "math.AG"
  ],
  "abstract": "In this paper we show how, given a complex of graded modules and knowing some partial Castelnuovo-Mumford regularities for all the modules in the complex and for all the positive homologies, it is possible to get a bound on the regularity of the zero homology. We use this to prove that if $\\dim \\tor_1^R(M,N)\\leq1$ then $\\reg(M\\otimes N)\\leq \\reg(M)+\\reg(N)$, generalizing results of Chandler, Conca and Herzog, and Sidman. Finally we give a description of the regularity of a module in terms of the postulation numbers of filter regular hyperplane restrictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-18T21:40:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13D45",
      "13D02"
    ],
    "keywords": [
      "castelnuovo-mumford regularity",
      "tensor products",
      "filter regular hyperplane restrictions",
      "partial castelnuovo-mumford regularities",
      "postulation numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10395C"
    }
  }
}