{
  "id": "math/0609456",
  "version": "v3",
  "published": "2006-09-15T23:53:13.000Z",
  "updated": "2007-03-20T04:45:37.000Z",
  "title": "Non-finiteness properties of fundamental groups of smooth projective varieties",
  "authors": [
    "Alexandru Dimca",
    "Stefan Papadima",
    "Alexander I. Suciu"
  ],
  "comment": "16 pages",
  "journal": "Journal f\\\"ur die reine und angewandte Mathematik 629 (2009), 89-105",
  "doi": "10.1515/crelle.2009.027",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "For each integer n\\ge 2, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n+1 and whose universal cover is a Stein manifold, homotopy equivalent to an infinite bouquet of n-dimensional spheres. This non-finiteness phenomenon is also reflected in the fact that the homotopy group \\pi_n(M), viewed as a module over Z\\pi_1(M), is free of infinite rank. As a result, we give a negative answer to a question of Koll'ar on the existence of quasi-projective classifying spaces (up to commensurability) for the fundamental groups of smooth projective varieties. To obtain our examples, we develop a complex analog of a method in geometric group theory due to Bestvina and Brady.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-03-20T04:45:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "57M07",
      "14H30",
      "20J05"
    ],
    "keywords": [
      "smooth projective varieties",
      "fundamental group",
      "non-finiteness properties",
      "geometric group theory",
      "universal cover"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9456D"
    }
  }
}