{
  "id": "2002.08250",
  "version": "v1",
  "published": "2020-02-19T15:52:11.000Z",
  "updated": "2020-02-19T15:52:11.000Z",
  "title": "On the position of nodes of plane curves",
  "authors": [
    "Cesar Lozano Huerta",
    "Tim Ryan"
  ],
  "comment": "6 pages. Comments or suggestions welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "The Severi variety $V_{d,n}$ of plane curves of a given degree $d$ and exactly $n$ nodes admits a map to the Hilbert scheme $\\mathbb{P}^{2[n]}$ of zero-dimensional subschemes of $\\mathbb{P}^2$ of degree $n$. This map assigns to every curve $C\\in V_{d,n}$ its nodes. For some $n$, we consider the image under this map of many known divisors of the Severi variety and its partial compactification. We compute the divisor classes of such images in Pic$(\\mathbb{P}^{2[n]})$ and provide enumerative numbers of nodal curves. We also answer directly a question of Diaz-Harris about whether the canonical class of the Severi variety is effective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-19T15:52:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "plane curves",
      "severi variety",
      "nodal curves",
      "divisor classes",
      "hilbert scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}