{
  "id": "1303.1653",
  "version": "v1",
  "published": "2013-03-07T11:53:22.000Z",
  "updated": "2013-03-07T11:53:22.000Z",
  "title": "K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups",
  "authors": [
    "Alice Garbagnati",
    "Matteo Penegini"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\\times C_2$ by the diagonal action of either the group $\\Z/p\\Z$ or the group $\\Z/2p\\Z$. These K3 surfaces admit a non-symplectic automorphism of order $p$ induced by an automorphism of one of the curves $C_1$ or $C_2$. We prove that most of the K3 surfaces admitting a non-symplectic automorphism of order $p$ (and in fact a maximal irreducible component of the moduli space of K3 surfaces with a non-symplectic automorphism of order $p$) are obtained in this way.\\\\ In addition, we show that one can obtain the same set of K3 surfaces under more restrictive assumptions namely one of the two curves, say $C_2$, is isomorphic to a rigid hyperelliptic curve with an automorphism $\\delta_p$ of order $p$ and the automorphism of the K3 surface is induced by $\\delta_p$.\\\\ Finally, we describe the variation of the Hodge structures of the surfaces constructed and we give an equation for some of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-07T11:53:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14J10",
      "14J50",
      "14D06"
    ],
    "keywords": [
      "non-symplectic automorphism",
      "cyclic groups",
      "product-quotient surfaces",
      "k3 surfaces admit",
      "rigid hyperelliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1653G"
    }
  }
}