{
  "id": "2005.04134",
  "version": "v1",
  "published": "2020-05-08T16:24:24.000Z",
  "updated": "2020-05-08T16:24:24.000Z",
  "title": "On the Severi problem in arbitrary characteristic",
  "authors": [
    "Karl Christ",
    "Xiang He",
    "Ilya Tyomkin"
  ],
  "comment": "34 pages, 9 figures. Comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that Severi varieties parametrizing irreducible reduced planar curves of given degree and geometric genus are either empty or irreducible in any characteristic. As a consequence, we generalize Zariski's theorem to positive characteristic and show that a general reduced planar curve of given geometric genus is nodal. As a byproduct, we obtain the first proof of the irreducibility of the moduli space of smooth projective curves of given genus in positive characteristic, that does not involve a reduction to the characteristic zero case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-08T16:24:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H10",
      "14H50",
      "14T05"
    ],
    "keywords": [
      "arbitrary characteristic",
      "severi problem",
      "irreducible reduced planar curves",
      "parametrizing irreducible reduced planar",
      "geometric genus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}