{
  "id": "1703.02127",
  "version": "v1",
  "published": "2017-03-06T22:01:58.000Z",
  "updated": "2017-03-06T22:01:58.000Z",
  "title": "On the arithmetic of a family of degree-two K3 surfaces",
  "authors": [
    "Florian Bouyer",
    "Edgar Costa",
    "Dino Festi",
    "Christopher Nicholls",
    "Mckenzie West"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $\\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\\mathcal{X}$ be the generic element of the family of surfaces in $\\mathbb{P}$ given by \\begin{equation*} X\\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \\end{equation*} The surface $\\mathcal{X}$ is a K3 surface over the function field $\\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\\mathcal{X}$ and other elements of the family $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-06T22:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G35",
      "14J28"
    ],
    "keywords": [
      "degree-two k3 surfaces",
      "arithmetic",
      "geometric picard lattice",
      "galois module structure",
      "function field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}