{
  "id": "0801.3423",
  "version": "v1",
  "published": "2008-01-22T17:27:12.000Z",
  "updated": "2008-01-22T17:27:12.000Z",
  "title": "Automorphism groups of algebraic curves with p-rank zero",
  "authors": [
    "Massimo Giulietti",
    "Gabor Korchmaros"
  ],
  "doi": "10.1112/jlms/jdp066",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "In positive characteristic, algebraic curves can have many more automorphisms than expected from the classical Hurwitz's bound. There even exist algebraic curves of arbitrary high genus g with more than 16g^4 automorphisms. It has been observed on many occasions that the most anomalous examples invariably have zero p-rank. In this paper, the K-automorphism group Aut(X) of a zero 2-rank algebraic curve X defined over an algebraically closed field K of characteristic 2 is investigated. The main result is that if the curve has genus g greater than or equal to 2, and |Aut(X)|>24g^2, then Aut(X) has a fixed point on X, apart from few exceptions. In the exceptional cases the possibilities for Aut(X) and g are determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-22T17:27:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37"
    ],
    "keywords": [
      "algebraic curve",
      "automorphism groups",
      "p-rank zero",
      "k-automorphism group aut",
      "arbitrary high genus"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3423G"
    }
  }
}