{
  "id": "math/0409348",
  "version": "v1",
  "published": "2004-09-20T18:58:07.000Z",
  "updated": "2004-09-20T18:58:07.000Z",
  "title": "A Septic with 99 real Nodes",
  "authors": [
    "Oliver Labs"
  ],
  "comment": "11 pages, 4 figures. For more images/movies, see http://www.AlgebraicSurface.net",
  "categories": [
    "math.AG"
  ],
  "abstract": "We find a surface of degree 7 in real projective three-space P^3(R) with 99 real nodes within a family of surfaces with dihedral symmetry: First, we consider this family over some small prime fields, which allows us to test all possible parameter sets using computer algebra. In this way we find some examples of 99-nodal surfaces over some of these finite fields. Then, the examination of the geometry of these surfaces allows us to determine the parameters of a 99-nodal septic in characteristic zero. This narrows the possibilities for \\mu(7), the maximum number of nodes on a septic, to: 99 <= \\mu(7) <= 104. When reducing our surface modulo 5, we even obtain a 100-nodal septic in P^3(F_5).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-20T18:58:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "14Q10"
    ],
    "keywords": [
      "real nodes",
      "small prime fields",
      "real projective three-space",
      "maximum number",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9348L"
    }
  }
}