{
  "id": "2009.02767",
  "version": "v1",
  "published": "2020-09-06T16:13:03.000Z",
  "updated": "2020-09-06T16:13:03.000Z",
  "title": "Periods of cubic surfaces with the automorphism group of order 54",
  "authors": [
    "Vasily Bolbachan"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "To any cubic surface, one can associate a cubic threefold given by a triple cover of $\\mathbb P^3$ branched in this cubic surface. D. Allcock, J. Carlson, and D. Toledo used this construction to define the period map for cubic surfaces. It is interesting to calculate this map for some specific cubic surfaces. In this paper, we have calculated it in the case when the cubic surface is given by a triple covering of $\\mathbb P^2$ branched in a smooth elliptic curve. In this case, the periods can be expressed through periods of the corresponding elliptic curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-06T16:13:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "triple cover",
      "smooth elliptic curve",
      "specific cubic surfaces",
      "cubic threefold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}