{
  "id": "1207.3526",
  "version": "v3",
  "published": "2012-07-15T16:00:37.000Z",
  "updated": "2014-09-16T14:18:39.000Z",
  "title": "A new family of surfaces with $p_g=q=2$ and $K^2=6$ whose Albanese map has degree $4$",
  "authors": [
    "Matteo Penegini",
    "Francesco Polizzi"
  ],
  "comment": "23 pages. To appear in the Journal of the London Mathematical Society. This is a preprint version, slightly different from the published version",
  "doi": "10.1112/jlms/jdu048",
  "categories": [
    "math.AG"
  ],
  "abstract": "We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible component of the moduli space of surfaces with $p_g=q=2$ and $K^2=6$. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the 2-dimensional family of product-quotient examples previously constructed by the first author. The main tools we use are the Fourier-Mukai transform and the Schr\\\"odinger representation of the finite Heisenberg group $\\mathscr{H}_3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-07T16:05:49.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-09-16T14:18:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10"
    ],
    "keywords": [
      "albanese map",
      "finite heisenberg group",
      "quadruple cover",
      "abelian surface",
      "moduli space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.3526P"
    }
  }
}