{
  "id": "2009.07880",
  "version": "v1",
  "published": "2020-09-16T18:20:30.000Z",
  "updated": "2020-09-16T18:20:30.000Z",
  "title": "The scrollar invariants of k-gonal curves having a nodal model on a smooth quadric having its nodes on few lines",
  "authors": [
    "Marc Coppens"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We determine the scrollar invariants of the normalization $C$ of a nodal curve $\\Gamma$ of type $(k,a)$ on a smooth quadric $\\mathbb{P}^1 \\times \\mathbb{P}^1$ associated to the $g^1_k$ defined by the pencil of lines of type $(0,1)$ in case all nodes are contained in at most $k-1$ lines of type $(1,0)$. This result is very much related to results obtained by E. Ballico, but in this paper the proof follows directly from an easy lemma. Also a result of E. Ballico on the existence of curves with prescribed scrollar invariant is a consequence of that lemma making the arguments much shorter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-16T18:20:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H51"
    ],
    "keywords": [
      "smooth quadric",
      "nodal model",
      "k-gonal curves",
      "nodal curve",
      "prescribed scrollar invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}