{
  "id": "1007.5036",
  "version": "v1",
  "published": "2010-07-28T17:27:00.000Z",
  "updated": "2010-07-28T17:27:00.000Z",
  "title": "Involutions on surfaces with $p_g=q=0$ and $K^2=3$",
  "authors": [
    "Carlos Rito"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study surfaces of general type $S$ with $p_g=0$ and $K^2=3$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$. It is shown that, if $S/i$ is not rational, then $S/i$ is birational to an Enriques surface or it has Kodaira dimension $1$ and the possibilities for the ramification divisor of the covering map $S\\rightarrow S/i$ are described. We also show that these two cases do occur, providing an example. In this example $S$ has a hyperelliptic fibration of genus $3$ and the bicanonical map of $S$ is of degree $2$ onto a rational surface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-28T17:27:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29"
    ],
    "keywords": [
      "involution",
      "bicanonical map",
      "enriques surface",
      "general type",
      "rational surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.5036R"
    }
  }
}