{
  "id": "0811.2407",
  "version": "v1",
  "published": "2008-11-14T19:24:19.000Z",
  "updated": "2008-11-14T19:24:19.000Z",
  "title": "Regularity of smooth curves in biprojective spaces",
  "authors": [
    "Victor Lozovanu"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Maclagan and Smith \\cite{MaclaganSmith} developed a multigraded version of Castelnuovo-Mumford regularity. Based on their definition we will prove in this paper that for a smooth curve $C\\subseteq \\P^a\\times\\P^b$ $(a, b\\geq 2)$ of bidegree $(d_1,d_2)$ with nondegenerate birational projections the ideal sheaf $\\mathcal{I}_{C|\\P^a\\times\\P^b}$ is $(d_2-b+1,d_1-a+1)$-regular. We also give an example showing that in some cases this bound is the best possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-14T19:24:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H45",
      "14F05"
    ],
    "keywords": [
      "smooth curve",
      "biprojective spaces",
      "nondegenerate birational projections",
      "castelnuovo-mumford regularity",
      "ideal sheaf"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.2407L"
    }
  }
}