{
  "id": "1507.03869",
  "version": "v1",
  "published": "2015-07-14T14:47:16.000Z",
  "updated": "2015-07-14T14:47:16.000Z",
  "title": "On the number of certain Del Pezzo surfaces of degree four violating the Hasse principle",
  "authors": [
    "Jörg Jahnel",
    "Damaris Schindler"
  ],
  "comment": "27 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give an asymptotic expansion for the density of del Pezzo surfaces of degree four in a certain Birch Swinnerton-Dyer family violating the Hasse principle due to a Brauer-Manin obstruction. Under the assumption of Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups for elliptic curves, we obtain an asymptotic formula for the number of all del Pezzo surfaces in the family, which violate the Hasse principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-14T14:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14G25",
      "14G05",
      "14J26",
      "14J10"
    ],
    "keywords": [
      "del pezzo surfaces",
      "hasse principle",
      "asymptotic expansion",
      "birch swinnerton-dyer",
      "brauer-manin obstruction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}