{
  "id": "0812.4518",
  "version": "v2",
  "published": "2008-12-24T11:01:15.000Z",
  "updated": "2010-07-07T17:22:15.000Z",
  "title": "The dihedral group $\\Dh_5$ as group of symplectic automorphisms on K3 surfaces",
  "authors": [
    "Alice Garbagnati"
  ],
  "comment": "11 pages. Arguments revised, results unchanged. Final version, to appear in Proc. Amer. Math. Soc",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove that if a K3 surface $X$ admits $\\Z/5\\Z$ as group of symplectic automorphisms, then it actually admits $\\Dh_5$ as group of symplectic automorphisms. The orthogonal complement to the $\\Dh_5$-invariants in the second cohomology group of $X$ is a rank 16 lattice, $L$. It is known that $L$ does not depend on $X$: we prove that it is isometric to a lattice recently described by R. L. Griess Jr. and C. H. Lam. We also give an elementary construction of $L$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-07T17:22:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J50"
    ],
    "keywords": [
      "symplectic automorphisms",
      "k3 surface",
      "dihedral group",
      "second cohomology group",
      "elementary construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4518G"
    }
  }
}