{
  "id": "1704.01100",
  "version": "v1",
  "published": "2017-04-04T16:44:40.000Z",
  "updated": "2017-04-04T16:44:40.000Z",
  "title": "On the canonical map of some surfaces isogenous to a product",
  "authors": [
    "Fabrizio Catanese"
  ],
  "comment": "29 pages, submitted to a volume dedicated to Lawrence Ein on the occasion of his 60th birthday",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "We give new contributions to the existence problem of canonical surfaces of high degree. We construct several families (indeed, connected components of the moduli space) of surfaces $S$ of general type with $p_g=5,6$ whose canonical map has image $\\Sigma$ of very high degree, $d=48$ for $p_g=5$, $d=56$ for $p_g=6$. And a connected component of the moduli space consisting of surfaces $S$ with $K^2_S = 40, p_g=4, q=0$ whose canonical map has always degree $\\geq 2$, and, for the general surface, of degree $2$ onto a canonical surface $Y$ with $K^2_Y = 12, p_g=4, q=0$. The surfaces we consider are SIP 's, i.e. surfaces $S$ isogenous to a product of curves $(C_1 \\times C_2 )/ G$; in our examples the group $G$ is elementary abelian, $G = (\\mathbb{Z}/m)^k$. We also establish some basic results concerning the canonical maps of any surface isogenous to a product, basing on elementary representation theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-04T16:44:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10",
      "14M07"
    ],
    "keywords": [
      "canonical map",
      "surfaces isogenous",
      "moduli space",
      "high degree",
      "canonical surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}