{
  "id": "1107.5535",
  "version": "v2",
  "published": "2011-07-27T16:49:18.000Z",
  "updated": "2013-04-23T09:04:04.000Z",
  "title": "The canonical ring of a 3-connected curve",
  "authors": [
    "Marco Franciosi",
    "Elisa Tenni"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let C be a projective curve either reduced with planar singularities or contained in a smooth algebraic surface. We show that the canonical ring R(C, \\omega_C)= \\oplus_{k \\geq 0} H^0(C, \\omega_C^k is generated in degree 1 if C is 3-connected and not (honestly) hyperelliptic; we show moreover that R(C, L)=\\oplus_{k \\geq 0} H^0(C,L^k)$ is generated in degree 1 if C is reduced with planar singularities and L is an invertible sheaf such that deg L_{|B} \\geq 2p_a(B)+1 for every B \\subseteq C.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-23T09:04:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H20",
      "14C20",
      "14H51"
    ],
    "keywords": [
      "canonical ring",
      "planar singularities",
      "smooth algebraic surface",
      "projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5535F"
    }
  }
}