{
  "id": "math/9910074",
  "version": "v3",
  "published": "1999-10-14T16:59:28.000Z",
  "updated": "2000-09-18T10:56:23.000Z",
  "title": "The bicanonical map of surfaces with $p_g=0$ and $K^2 \\geq 7$",
  "authors": [
    "M. Mendes Lopes",
    "R. Pardini"
  ],
  "comment": "LaTeX 2e, 15 pages, to appear. Minor typos, change of title (title of the previous version: \"A note on surfaces of general type with $p_g=0$ and $K^2\\ge 7$\") and added one example of a surface, showing that the main result is sharp",
  "categories": [
    "math.AG"
  ],
  "abstract": "A minimal surface of general type with $p_g(S)=0$ satisfies $1\\le K^2\\le 9$ and it is known that the image of the bicanonical map $\\fie$ is a surface for $K_S^2\\geq 2$, whilst for $K^2_S\\geq 5$, the bicanonical map is always a morphism. In this paper it is shown that $\\fie$ is birational if $K_S^2=9$ and that the degree of $\\fie$ is at most 2 if $K_S^2=7$ or $K_S^2=8$. By presenting two examples of surfaces $S$ with $K_S^2=7$ and 8 and bicanonical map of degree 2, it is also shown that this result is sharp. The example with $K_S^2=8$ is, to our knowledge, a new example of a surface of general type with $p_g=0$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-09-18T10:56:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bicanonical map",
      "general type",
      "minimal surface",
      "birational"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....10074M"
    }
  }
}