{
  "id": "1601.02408",
  "version": "v1",
  "published": "2016-01-11T11:34:04.000Z",
  "updated": "2016-01-11T11:34:04.000Z",
  "title": "On the existence of primitive pencils for smooth curves",
  "authors": [
    "E. Ballico"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $C$ be a smooth curve with gonality $k\\ge 6$ and genus $g\\ge 2k^2+5k-6$. We prove that $W^1_d({C})$ has the expected dimension and that the general element of any irreducible component of $W^1_d({C})$ is primitive if either $g-k+4\\le d\\le g-2$ or $d=g-k+3$ and either $k$ is odd or $C$ is not a double covering of a curve of gonality $k/2$ and genus $k-3$. Even in the latter case we prove the existence of a complete and primitive $g^1_{g-k+3}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-11T11:34:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H51"
    ],
    "keywords": [
      "smooth curve",
      "primitive pencils",
      "general element",
      "irreducible component"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102408B"
    }
  }
}