{
  "id": "2102.07285",
  "version": "v1",
  "published": "2021-02-15T00:40:43.000Z",
  "updated": "2021-02-15T00:40:43.000Z",
  "title": "Complex Multiplication and Noether-Lefschetz Loci of the Twistor Space of a K3 Surface",
  "authors": [
    "Francesco Viganò"
  ],
  "comment": "24 pages, 8 different figures (one of which repeating 4 times, one of which repeating 2 times)",
  "categories": [
    "math.AG"
  ],
  "abstract": "For an algebraic K3 surface with complex multiplication (CM), algebraic fibres of the associated twistor space away from the equator are again of CM type. In this paper, we show that algebraic fibres corresponding to points at the same altitude of the twistor base $S^2\\simeq \\mathbb{P}^1_\\mathbb{C}$ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-15T00:40:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28"
    ],
    "keywords": [
      "complex multiplication",
      "noether-lefschetz loci",
      "algebraic fibres",
      "algebraic k3 surface",
      "associated twistor space away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}