{
  "id": "1512.08839",
  "version": "v1",
  "published": "2015-12-30T04:00:51.000Z",
  "updated": "2015-12-30T04:00:51.000Z",
  "title": "Fundamental Group of some Genus-2 Fibrations and Applications",
  "authors": [
    "R. V. Gurjar",
    "Sagar Kolte"
  ],
  "comment": "23 Pages, Published in the International Journal of Mathematics",
  "doi": "10.1142/S0129167X12500802",
  "categories": [
    "math.AG"
  ],
  "abstract": "We will prove that given a genus-2 fibration $f: X \\rightarrow C$ on a smooth projective surface $X$ such that $b_1(X)=b_1(C)+2$, the fundamental group of $X$ is almost isomorphic to $\\pi_1(C) \\times \\pi_1(E)$, where $E$ is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces $X$ with genus-2 fibration $X\\rightarrow C$ such that $b_1(X)>b_1(C)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-30T04:00:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "14H30"
    ],
    "keywords": [
      "fundamental group",
      "applications",
      "universal cover",
      "smooth projective surface",
      "holomorphic convexity"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "World Scientific"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151208839G"
    }
  }
}