{
  "id": "2403.17167",
  "version": "v1",
  "published": "2024-03-25T20:33:03.000Z",
  "updated": "2024-03-25T20:33:03.000Z",
  "title": "Monodromy groups of indecomposable coverings of bounded genus",
  "authors": [
    "Danny Neftin",
    "Michael E. Zieve"
  ],
  "categories": [
    "math.AG",
    "math.GR",
    "math.NT"
  ],
  "abstract": "For each nonnegative integer $g$, we classify the ramification types and monodromy groups of indecomposable coverings of complex curves $f: X\\to Y$ where $X$ has genus $g$, under the hypothesis that $n:=\\deg(f)$ is sufficiently large and the monodromy group is not $A_n$ or $S_n$. This proves a conjecture of Guralnick and several conjectures of Guralnick and Shareshian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-25T20:33:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G99",
      "14E20",
      "20B15",
      "12F10"
    ],
    "keywords": [
      "monodromy group",
      "indecomposable coverings",
      "bounded genus",
      "complex curves",
      "ramification types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}