{
  "id": "math/0402154",
  "version": "v1",
  "published": "2004-02-10T13:50:11.000Z",
  "updated": "2004-02-10T13:50:11.000Z",
  "title": "The Cox Ring of a Del Pezzo Surface Has Rational Singularities",
  "authors": [
    "Oleg N. Popov"
  ],
  "comment": "12 pages, LateX, uses XY-Pic",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, called the Cox ring. We show that in characteristic 0 this ring is Gorenstein and its spectrum has rational singularities. Also a gap in math.AG/0309111 is pointed out.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-10T13:50:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14J17"
    ],
    "keywords": [
      "rational singularities",
      "cox ring",
      "smooth del pezzo surface",
      "direct sum",
      "isomorphism classes"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2154P"
    }
  }
}