{
  "id": "math/0202131",
  "version": "v1",
  "published": "2002-02-14T05:27:43.000Z",
  "updated": "2002-02-14T05:27:43.000Z",
  "title": "Automorphisms of finite order on Gorenstein del Pezzo surfaces",
  "authors": [
    "D. -Q. Zhang"
  ],
  "comment": "18 pages, Transactions of the American Mathematical Society, to appear",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this note we shall determine all actions of groups of prime order p with p > 3 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show that every order-p element in Aut(Y) (= Aut(Y'), Y' being the minimal resolution of Y) is lifted from a projective transformation of the projective plane. We also determine when Aut(Y) is finite in terms of the self intersection of the canonical divisor of Y, Sing(Y) and the number of singular members in the anti-canonical linear system of Y. In particular, we show that either |Aut(Y)| = 2^a 3^b for some 0 < a+b < 8, or for every prime p > 3 there is at least one element g_p of order p in Aut(Y) (hence |Aut(Y)| is infinite).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-14T05:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14J26"
    ],
    "keywords": [
      "gorenstein del pezzo surfaces",
      "finite order",
      "automorphisms",
      "picard number",
      "linear system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2131Z"
    }
  }
}