{
  "id": "1010.3897",
  "version": "v3",
  "published": "2010-10-19T13:12:26.000Z",
  "updated": "2012-07-12T19:03:00.000Z",
  "title": "Two moduli spaces of abelian fourfolds with an automorphism of order five",
  "authors": [
    "Bert van Geemen",
    "Matthias Schuett"
  ],
  "comment": "27 pages; v3: 4.5 corrected",
  "categories": [
    "math.AG"
  ],
  "abstract": "We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarised abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in IP^4 which is the complete intersection of two S_5-invariant cubics. It is dominated by a Hilbert modular surface and we give a modular interpretation for this. We also determine the L-series of these varieties as well as those of several modular covers of the Shimura curve.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-12T19:03:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli spaces",
      "automorphism",
      "compact shimura curve",
      "hilbert modular surface",
      "principally polarised abelian fourfolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.3897V"
    }
  }
}