{
  "id": "math/0210005",
  "version": "v1",
  "published": "2002-10-01T08:40:31.000Z",
  "updated": "2002-10-01T08:40:31.000Z",
  "title": "Algebraic surfaces with quotient singularities - including some discussion on automorphisms and fundamental groups",
  "authors": [
    "J. Keum",
    "D. -Q. Zhang"
  ],
  "comment": "26 pages, Proc. Alg. Geom. in East Asia, Kyoto, 3-10 Aug 2001, A. Ohbuchi et al (eds), to appear",
  "categories": [
    "math.AG"
  ],
  "abstract": "We survey some recent progress in the study of algebraic varieties X with log terminal singularities, especially, the uni-ruledness of the smooth locus X^0 of X, the fundamental group of X^0 and the automorphisms group on (smooth or singular) X when dim X = 2. The full automorphism groups of a few interesting types of K3 surfaces are described, mainly by Keum-Kondo. We conjecture that when X is Q-Fano then X^0 has a finite fundamental group, which had been proved if either dim X < 3 or the Fano index is bigger than dim X - 2. We also conjecture that when X is a log Enriques (e.g. a normal K3 or a normal Enriques) surface then either pi_1(X^0) is finite or X has an abelian surface as its quasi-etale cover, which has been proved by Catanese-Keum-Oguiso under some extra conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-01T08:40:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J17",
      "14J50",
      "14F35"
    ],
    "keywords": [
      "algebraic surfaces",
      "quotient singularities",
      "discussion",
      "full automorphism groups",
      "finite fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10005K"
    }
  }
}