{
  "id": "2011.10181",
  "version": "v1",
  "published": "2020-11-20T02:37:40.000Z",
  "updated": "2020-11-20T02:37:40.000Z",
  "title": "Rational curves on K3 surfaces of small genus",
  "authors": [
    "Rijul Saini"
  ],
  "comment": "53 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\mathfrak B_g$ denote the moduli space of primitively polarized $K3$ surfaces $(S,H)$ of genus $g$ over $\\mathbb C$. It is well-known that $\\mathfrak B_g$ is irreducible and that there are only finitely many rational curves in $|H|$ for any primitively polarized $K3$ surface $(S,H)$. So we can ask the question of finding the monodromy group of such curves. The case of $g=2$ essentially follows from the results of Harris \\cite{Ha} to be the full symmetric group $S_{324}$, here we solve the case $g=3$ and $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-20T02:37:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "20B25",
      "14H45"
    ],
    "keywords": [
      "rational curves",
      "k3 surfaces",
      "small genus",
      "full symmetric group",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}