{
  "id": "math/0509529",
  "version": "v1",
  "published": "2005-09-22T18:52:09.000Z",
  "updated": "2005-09-22T18:52:09.000Z",
  "title": "Degenerations of del Pezzo surfaces I",
  "authors": [
    "Paul Hacking",
    "Yuri Prokhorov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a surface with quotient singularities which admits a smoothing to the plane. We prove that X is a deformation of a weighted projective plane P(a^2,b^2,c^2), where a,b,c is a solution of the Markov equation a^2+b^2+c^2=3abc. We also prove a generalisation for del Pezzo surfaces of degree K^2 at least 5.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-09-22T18:52:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14E30"
    ],
    "keywords": [
      "del pezzo surfaces",
      "degenerations",
      "quotient singularities",
      "markov equation",
      "deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9529H"
    }
  }
}