{
  "id": "1203.4520",
  "version": "v5",
  "published": "2012-03-20T17:19:07.000Z",
  "updated": "2014-02-26T19:20:35.000Z",
  "title": "Low dimensional projective groups",
  "authors": [
    "Indranil Biswas",
    "Mahan Mj"
  ],
  "comment": "This paper is withdrawn due to a crucial gap in the proof of Theorem 4.7. This step in the proof goes through only in the presence of an extra cohomology vanishing condition",
  "categories": [
    "math.GT",
    "math.AG"
  ],
  "abstract": "We initiate the study of holomorphically convex groups: groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers. If $G$ is a holomorphically convex group of cohomological dimension two, we show that $G$ is isomorphic to the fundamental group of a compact Riemann surface. As a consequence, we show that if a linear group $G$ has (rational) cohomological dimension two and is the fundamental group of a smooth complex projective variety, then $G$ is a (virtual) surface group.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-02-26T19:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M50",
      "32Q15",
      "57M05",
      "14F35",
      "32J15"
    ],
    "keywords": [
      "low dimensional projective groups",
      "smooth complex projective variety",
      "fundamental group",
      "holomorphically convex group",
      "holomorphically convex universal covers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.4520B"
    }
  }
}