{
  "id": "math/9901128",
  "version": "v1",
  "published": "1999-01-27T13:52:14.000Z",
  "updated": "1999-01-27T13:52:14.000Z",
  "title": "A Note on a Conjecture of Xiao",
  "authors": [
    "Miguel A. Barja",
    "Francesco Zucconi"
  ],
  "comment": "2 pages; Latex",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of $f$ is ample when the slope of the fibration is less than 4, if the general fibre of $f$ is non-hyperelliptic or the genus of the fibre or of the base curve is low.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-01-27T13:52:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14J10"
    ],
    "keywords": [
      "conjecture",
      "relatively minimal fibred surface",
      "partial affirmative answer",
      "direct image",
      "general fibre"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......1128B"
    }
  }
}