{
  "id": "1410.5671",
  "version": "v1",
  "published": "2014-10-21T14:12:11.000Z",
  "updated": "2014-10-21T14:12:11.000Z",
  "title": "The Hasse principle for lines on del Pezzo surfaces",
  "authors": [
    "Jörg Jahnel",
    "Daniel Loughran"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper, we consider the following problem: Does there exist a cubic surface over $\\mathbb{Q}$ which contains no line over $\\mathbb{Q}$, yet contains a line over every completion of $\\mathbb{Q}$? This question may be interpreted as asking whether the Hilbert scheme of lines on a cubic surface can fail the Hasse principle. We also consider analogous problems, over arbitrary number fields, for other del Pezzo surfaces and complete intersections of two quadrics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-21T14:12:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "11R32",
      "14J26",
      "14-04"
    ],
    "keywords": [
      "del pezzo surfaces",
      "hasse principle",
      "cubic surface",
      "arbitrary number fields",
      "hilbert scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5671J"
    }
  }
}