{
  "id": "2209.13003",
  "version": "v1",
  "published": "2022-09-26T20:37:22.000Z",
  "updated": "2022-09-26T20:37:22.000Z",
  "title": "One-dimensional Local Families of Complex K3 Surfaces",
  "authors": [
    "Riccardo Carini",
    "Francesco Viganò"
  ],
  "comment": "10 pages, 4 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "For any complex K3 surface $X$, we construct a one-dimensional deformation in which all integers $\\rho$ with $0 \\leq \\rho \\leq 20$ occur as Picard numbers of some fibres. In contrast, we prove that the generic one-dimensional local family of K3 surfaces admits only $0$ and $1$ as Picard numbers of the fibres.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-26T20:37:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28"
    ],
    "keywords": [
      "complex k3 surface",
      "picard numbers",
      "k3 surfaces admits",
      "one-dimensional deformation",
      "generic one-dimensional local family"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}