{
  "id": "2004.09093",
  "version": "v1",
  "published": "2020-04-20T07:17:31.000Z",
  "updated": "2020-04-20T07:17:31.000Z",
  "title": "The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations",
  "authors": [
    "Tulin Altunoz"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "We consider complex surfaces, viewed as smooth $4$-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the $2$-sphere. In this paper, we show that the minimal number of singular fibers of such fibrations is equal to $2g+4$ for even $g\\geq4$. For odd $g\\geq7$, we show that the number is greater than or equal to $2g+6$. Moreover, we discuss the minimal number of singular fibers in all hyperelliptic Lefschetz fibrations over the $2$-sphere as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-20T07:17:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular fibers",
      "admit hyperelliptic lefschetz fibrations",
      "minimal number",
      "dimensional manifolds",
      "complex surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}