{
  "id": "math/0502520",
  "version": "v1",
  "published": "2005-02-24T16:52:10.000Z",
  "updated": "2005-02-24T16:52:10.000Z",
  "title": "A Sextic with 35 Cusps",
  "authors": [
    "Oliver Labs"
  ],
  "comment": "6 pages, 1 figure, for additional images/movies, see http://www.AlgebraicSurface.net",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Recently, W. Barth and S. Rams discussed sextics with up to 30 $A_2$-singularities (also called cusps) and their connection to coding theory [math.AG/0403018]. In the present paper, we find a sextic with 35 cusps within a four-parameter family of surfaces of degree 6 in projective three-space with dihedral symmetry $D_5$. This narrows the possibilities for the maximum number $\\mu_{A_2}(6)$ of $A_2$-singularities on a sextic to $35 \\le \\mu_{A_2}(6) \\le 37$. To construct this surface, we use a general algorithm in characteristic zero for finding hypersurfaces with many singularities within a family.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-24T16:52:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "14Q10"
    ],
    "keywords": [
      "singularities",
      "dihedral symmetry",
      "maximum number",
      "general algorithm",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2520L"
    }
  }
}