{
  "id": "math/0210021",
  "version": "v1",
  "published": "2002-10-02T09:25:48.000Z",
  "updated": "2002-10-02T09:25:48.000Z",
  "title": "On Endomorphisms of Algebraic Surfaces",
  "authors": [
    "D. -Q. Zhang"
  ],
  "comment": "15 pages, Contemporary Math. Amer. Math. Soc. to appear",
  "categories": [
    "math.AG"
  ],
  "abstract": "In these notes, we consider self-maps of degree > 1 on a weak del Pezzo surface X of degree < 8. We show that there are exactly 12 such X, modulo isomorphism. In particular, K_X^2 > 2, and if X has one self-map of degree > 1 then for every positive integer d there is a self-map of degree d^2 on X. We prove the Sato conjecture in the present case, the general case of which has been proved by N. Nakayama.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-02T09:25:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J26",
      "14E20"
    ],
    "keywords": [
      "algebraic surfaces",
      "endomorphisms",
      "weak del pezzo surface",
      "sato conjecture",
      "general case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10021Z"
    }
  }
}