{
  "id": "math/0409526",
  "version": "v1",
  "published": "2004-09-27T15:56:55.000Z",
  "updated": "2004-09-27T15:56:55.000Z",
  "title": "A note on the very ampleness of complete linear systems on blowings-up of P^3",
  "authors": [
    "Cindy De Volder",
    "Antonio Laface"
  ],
  "comment": "6 pages, LaTeX",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this note we consider the blowing-up X of P^3 along r general points of the anticanonical divisor of a smooth quadric in P^3. Given a complete linear system |L| = |dH - m_1 E_1 -...- m_r E_r| on X, with H the pull-back of a plane in P^3 and E_i the exceptional divisor corresponding to P_i, we give necessary and sufficient conditions for the very ampleness (resp. base point freeness and non-speciality) of L. As a corollary we obtain a sufficient condition for the very ampleness of such a complete linear system on the blowing-up of P^3 along r general points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-27T15:56:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20"
    ],
    "keywords": [
      "complete linear system",
      "general points",
      "sufficient condition",
      "blowings-up",
      "base point freeness"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9526D"
    }
  }
}