{
  "id": "2004.08719",
  "version": "v1",
  "published": "2020-04-18T22:42:22.000Z",
  "updated": "2020-04-18T22:42:22.000Z",
  "title": "Monodromy of rational curves on K3 surfaces of low genus",
  "authors": [
    "Sailun Zhan"
  ],
  "comment": "23 pages. Comments are very welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "The monodromy group of the flexes or bitangents of a generic plane curve, the monodromy group of the lines on a generic degree $2n-3$ hypersurface in $\\mathbb{P}^{n}$, and the monodromy group of the conics tangent to five generic conics are well-studied. In most cases, these monodromy groups are the full symmetric groups. We study a similar phenomenon on the rational curves in $|\\mathcal{O}(1)|$ on a generic K3 surface. We prove that when the K3 surface has genus $g$, $1\\leq g\\leq 3$, the monodromy group is also the full symmetric group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-18T22:42:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D05",
      "14J20",
      "14J28",
      "14N10"
    ],
    "keywords": [
      "monodromy group",
      "rational curves",
      "low genus",
      "full symmetric group",
      "generic plane curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}