{
  "id": "0806.1336",
  "version": "v2",
  "published": "2008-06-08T16:26:30.000Z",
  "updated": "2012-09-06T17:03:17.000Z",
  "title": "On Discrete Subgroups of automorphism of $P^2_C$",
  "authors": [
    "Angel Cano",
    "José Seade"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the geometry and dynamics of discrete subgroups $\\Gamma$ of $\\PSL(3,\\mathbb{C})$ with an open invariant set $\\Omega \\subset \\PC^2$ where the action is properly discontinuous and the quotient $\\Omega/\\Gamma$ contains a connected component whicis compact. We call such groups {\\it quasi-cocompact}. In this case $\\Omega/\\Gamma$ is a compact complex projective orbifold and $\\Omega$ is a {\\it divisible set}. Our first theorem refines classical work by Kobayashi-Ochiai and others about complex surfaces with a projective structure: We prove that every such group is either virtually affine or complex hyperbolic. We then classify the divisible sets that appear in this way, the corresponding quasi-cocompact groups and the orbifolds $\\Omega/\\Gamma$. We also prove that excluding a few exceptional cases, the Kulkarni region of discontinuity coincides with the equicontinuity region and is the largest open invariant set where the action is properly discontinuous.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-06T17:03:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F99"
    ],
    "keywords": [
      "discrete subgroups",
      "largest open invariant set",
      "first theorem refines classical work",
      "automorphism",
      "connected component whicis compact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1336C"
    }
  }
}