{
  "id": "1410.8065",
  "version": "v1",
  "published": "2014-10-29T17:27:03.000Z",
  "updated": "2014-10-29T17:27:03.000Z",
  "title": "On linear systems of P^3 with nine base points",
  "authors": [
    "Maria Chiara Brambilla",
    "Olivia Dumitrescu",
    "Elisa Postinghel"
  ],
  "comment": "24 pages. arXiv admin note: text overlap with arXiv:0812.0032 by other authors",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We study special linear systems of surfaces of P^3 interpolating nine points in general position having a quadric as fixed component. By performing degenerations in the blown-up space, we interpret the quadric obstruction in terms of linear obstructions for a quasi-homogeneous class. By degeneration we also prove a Nagata type result for P^2 that implies a base locus lemma for the quadric. As an application we establish Laface-Ugaglia Conjecture for linear systems with multiplicities bounded by 8 and for homogeneous linear systems with multiplicity m and degree up to 2m+1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-29T17:27:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C20",
      "14J70",
      "14J26"
    ],
    "keywords": [
      "base points",
      "study special linear systems",
      "base locus lemma",
      "nagata type result",
      "blown-up space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.8065C"
    }
  }
}