{
  "id": "1703.10646",
  "version": "v1",
  "published": "2017-03-30T19:30:05.000Z",
  "updated": "2017-03-30T19:30:05.000Z",
  "title": "A pair of rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not the bidisk",
  "authors": [
    "Francesco Polizzi",
    "Carlos Rito",
    "Xavier Roulleau"
  ],
  "comment": "24 pages, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "We construct two complex-conjugated rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces with these invariants and Albanese map of degree $2$, apart the family of product-quotient surfaces constructed by Penegini. This completes the classification of surfaces with $p_g=q=2, K^2=8$ and Albanese map of degree $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-30T19:30:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10"
    ],
    "keywords": [
      "universal cover",
      "albanese map",
      "unique surfaces",
      "product-quotient surfaces",
      "complex-conjugated rigid surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}