{
  "id": "1408.2254",
  "version": "v1",
  "published": "2014-08-10T17:01:22.000Z",
  "updated": "2014-08-10T17:01:22.000Z",
  "title": "Notes on automorphisms of surfaces of general type with $p_g=0$ and $K^2=7$",
  "authors": [
    "Yifan Chen"
  ],
  "comment": "14 pages, 2 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue surface with $K^2=7$ is isomorphic to $\\mathbb{Z}_2^2$ or $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$. We construct a $2$-dimensional family of Inoue surfaces with automorphism groups isomorphic to $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-10T17:01:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J50"
    ],
    "keywords": [
      "general type",
      "inoue surface",
      "smooth minimal complex surface",
      "automorphism groups isomorphic",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2254C"
    }
  }
}