{
  "id": "math/0310342",
  "version": "v1",
  "published": "2003-10-21T16:17:49.000Z",
  "updated": "2003-10-21T16:17:49.000Z",
  "title": "A Complex Ball Uniformization of the Moduli Space of Cubic Surfaces Via Periods of K3 Surfaces",
  "authors": [
    "I. Dolgachev",
    "B. van Geemen",
    "S. Kondo"
  ],
  "comment": "47 pages, LaTeX",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K3 surfaces which are naturally associated to cubic surfaces. A similar uniformization is given for the covers of the moduli space corresponding to geometric markings of the Picard group or to the choice of a line on the surface. We also give a detailed description of the boundary components corresponding to singular surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-21T16:17:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "14J10",
      "14J28"
    ],
    "keywords": [
      "complex ball uniformization",
      "moduli space",
      "k3 surfaces",
      "nodal cubic surfaces",
      "boundary components"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10342D"
    }
  }
}