{
  "id": "1802.06333",
  "version": "v1",
  "published": "2018-02-18T05:15:29.000Z",
  "updated": "2018-02-18T05:15:29.000Z",
  "title": "Explicit equations of a fake projective plane",
  "authors": [
    "Lev A. Borisov",
    "JongHae Keum"
  ],
  "comment": "This is a full version of \"Research announcement: equations of a fake projective plane\", arXiv:1710.04501",
  "categories": [
    "math.AG"
  ],
  "abstract": "Fake projective planes are smooth complex surfaces of general type with Betti numbers equal to those of the usual projective plane. They come in complex conjugate pairs and have been classified as quotients of the two-dimensional ball by explicitly written arithmetic subgroups. In this paper we find equations of a projective model of a conjugate pair of fake projective planes by studying the geometry of the quotient of such surface by an order seven automorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-18T05:15:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14F05",
      "32Q40",
      "32N15"
    ],
    "keywords": [
      "fake projective plane",
      "explicit equations",
      "complex conjugate pairs",
      "smooth complex surfaces",
      "explicitly written arithmetic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}