{
  "id": "0803.0353",
  "version": "v2",
  "published": "2008-03-03T23:57:28.000Z",
  "updated": "2009-09-17T03:03:06.000Z",
  "title": "Cox rings of degree one del Pezzo surfaces",
  "authors": [
    "Damiano Testa",
    "Anthony Várilly-Alvarado",
    "Mauricio Velasco"
  ],
  "comment": "Significant revision. Proposition 4.4 fixes gap in previous version. To appear in Algebra and Number Theory",
  "journal": "Algebra and Number Theory 3 (2009) 729-761.",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Let X be a del Pezzo surface of degree one over an algebraically closed field (of any characteristic), and let Cox(X) be its total coordinate ring. We prove the missing case of a conjecture of Batyrev and Popov, which states that Cox(X) is a quadratic algebra. We use a complex of vector spaces whose homology determines part of the structure of the minimal free Pic(X)-graded resolution of Cox(X) over a polynomial ring. We show that sufficiently many Betti numbers of this minimal free resolution vanish to establish the conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-09-17T03:03:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26"
    ],
    "keywords": [
      "del pezzo surface",
      "cox rings",
      "homology determines part",
      "minimal free pic",
      "minimal free resolution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0353T"
    }
  }
}