{
  "id": "2106.09988",
  "version": "v1",
  "published": "2021-06-18T08:18:05.000Z",
  "updated": "2021-06-18T08:18:05.000Z",
  "title": "Singularities of normal quartic surfaces I (char=2)",
  "authors": [
    "Fabrizio Catanese"
  ],
  "comment": "22 pages, Dedicated to Bernd Sturmfels on the occasion of his 60-th birthday. Improves on the main result of the previous paper by the author arXiv:2106.06643, which has a big overlapping with the present paper, but is not completely superseded",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show, in this first part, that the maximal number of singular points of a quartic surface $X \\subset \\mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $18$. We produce examples with $14$ singular points, and show that, under several geometric assumptions ($\\mathfrak S_4$-symmetry, or behaviour of the Gauss map, or structure of tangent cone at one of the singular points $P$ , separability/inseparability of the projection with centre $P$), we obtain better upper bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-18T08:18:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "14J25",
      "14J28",
      "14N05"
    ],
    "keywords": [
      "normal quartic surfaces",
      "singular points",
      "singularities",
      "better upper bounds",
      "produce examples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}