{
  "id": "2401.04072",
  "version": "v1",
  "published": "2024-01-08T18:18:33.000Z",
  "updated": "2024-01-08T18:18:33.000Z",
  "title": "K3 surfaces with real or complex multiplication",
  "authors": [
    "Eva Bayer-Fluckiger",
    "Bert van Geemen",
    "Matthias Schütt"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $E$ be a totally real number field of degree $d$ and let $m \\geq 3$ be an integer. We show that if $md \\leq 21$ then there exists an $m-2$-dimensional family of complex projective $K3$ surfaces with real multiplication by $E$. An analogous result is proved for CM number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T18:18:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex multiplication",
      "k3 surfaces",
      "cm number fields",
      "totally real number field",
      "real multiplication"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}