{
  "id": "math/9910012",
  "version": "v1",
  "published": "1999-10-04T12:40:27.000Z",
  "updated": "1999-10-04T12:40:27.000Z",
  "title": "A connected component of the moduli space of surfaces of general type with $p_g=0$",
  "authors": [
    "M. Mendes Lopes",
    "R. Pardini"
  ],
  "comment": "LaTeX 2.09, 20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $\\phi:S\\to \\pp^{K^2_S}$ is a morphism: then the degree of $\\phi$ is at most 4 and if it is equal to 4 then $K^2_S\\le 6$. Here we prove that if $K^2_S=6$ and $\\deg \\phi=4$ then S is a so-called {\\em Burniat surface}. In addition we show that minimal surfaces with $p_g=0$, $K^2=6$ and bicanonical map of degree 4 form a 4-dimensional irreducible connected component of the moduli space of surfaces of general type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-10-04T12:40:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10"
    ],
    "keywords": [
      "general type",
      "moduli space",
      "minimal surface",
      "bicanonical map",
      "burniat surface"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....10012M"
    }
  }
}