{
  "id": "0705.0476",
  "version": "v1",
  "published": "2007-05-03T14:40:02.000Z",
  "updated": "2007-05-03T14:40:02.000Z",
  "title": "Automorphism groups and anti-pluricanonical curves",
  "authors": [
    "De-Qi Zhang"
  ],
  "comment": "Mathematical Research Letters (to appear); 20 pages",
  "categories": [
    "math.AG",
    "math.DS"
  ],
  "abstract": "We show the existence of an anti-pluricanonical curve on every smooth projective rational surface X which has an infinite group G of automorphisms of either null entropy or of type Z . Z (semi-direct product), provided that the pair (X, G) is minimal. This was conjectured by Curtis T. McMullen (2005) and further traced back to Marat Gizatullin and Brian Harbourne (1987). We also prove (perhaps) the strongest form of the famous Tits alternative theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-03T14:40:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14J50",
      "37B40",
      "32H50"
    ],
    "keywords": [
      "anti-pluricanonical curve",
      "automorphism groups",
      "smooth projective rational surface",
      "infinite group",
      "null entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.0476Z"
    }
  }
}