{
  "id": "math/0003153",
  "version": "v1",
  "published": "2000-03-24T18:03:26.000Z",
  "updated": "2000-03-24T18:03:26.000Z",
  "title": "Gorenstein models of del Pezzo surfaces of degree 1 over Dedekind schemes",
  "authors": [
    "Mikhail Grinenko"
  ],
  "comment": "11 pages, AmsLaTex, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let R be a Dedekind scheme, $\\nu$ its generic point, X and V del Pezzo surfaces of degree 1 over R that are Gorenstein Mori fiber spaces (as 3-folds germs over the ground field). We study birational maps $\\phi:X\\dasharrow V$ over R which are isomorphisms over the generic point of R. We put down normal forms of such transformations (in suitable coordinates) and give some properties of X and V. In particular, we prove the uniqueness of a smooth model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-03-24T18:03:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E06",
      "14E07"
    ],
    "keywords": [
      "del pezzo surfaces",
      "dedekind scheme",
      "gorenstein models",
      "generic point",
      "gorenstein mori fiber spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......3153G"
    }
  }
}