{
  "id": "1102.3443",
  "version": "v3",
  "published": "2011-02-16T22:12:39.000Z",
  "updated": "2012-04-23T22:21:21.000Z",
  "title": "On the order of an automorphism of a smooth hypersurface",
  "authors": [
    "Víctor González-Aguilera",
    "Alvaro Liendo"
  ],
  "journal": "Israel J. Math. 197 (2013), no. 1, 29-49",
  "doi": "10.1007/s11856-012-0177-y",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we give an effective criterion as to when a positive integer q is the order of an automorphism of a smooth hypersurface of dimension n and degree d, for every d>2, n>1, (n,d)\\neq (2,4), and \\gcd(q,d)=\\gcd(q,d-1)=1. This allows us to give a complete criterion in the case where q=p is a prime number. In particular, we show the following result: If X is a smooth hypersurface of dimension n and degree d admitting an automorphism of prime order p then p<(d-1)^{n+1}; and if p>(d-1)^n then X is isomorphic to the Klein hypersurface, n=2 or n+2 is prime, and p=\\Phi_{n+2}(1-d) where \\Phi_{n+2} is the (n+2)-th cyclotomic polynomial. Finally, we provide some applications to intermediate jacobians of Klein hypersurfaces.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-04-23T22:21:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J40",
      "14J30"
    ],
    "keywords": [
      "smooth hypersurface",
      "automorphism",
      "klein hypersurface",
      "complete criterion",
      "prime number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3443G"
    }
  }
}