{
  "id": "1907.05684",
  "version": "v1",
  "published": "2019-07-12T11:49:39.000Z",
  "updated": "2019-07-12T11:49:39.000Z",
  "title": "The boundary of the $p$-rank $0$ stratum of the moduli space of cyclic covers of the projective line",
  "authors": [
    "Ekin Ozman",
    "Rachel Pries",
    "Colin Weir"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the $p$-rank stratification of the moduli space of cyclic degree $\\ell$ covers of the projective line in characteristic $p$ for distinct primes $p$ and $\\ell$. The main result is about the intersection of the $p$-rank $0$ stratum with the boundary of the moduli space of curves. When $\\ell=3$ and $p \\equiv 2 \\bmod 3$ is an odd prime, we prove that there exists a smooth trielliptic curve in characteristic $p$, with every genus $g$, signature type $(r,s)$ and $p$-rank $f$ satisfying the clear necessary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-12T11:49:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G20",
      "14D20",
      "14H10",
      "14H40",
      "11G10",
      "14H30",
      "14H37",
      "14K10"
    ],
    "keywords": [
      "moduli space",
      "projective line",
      "cyclic covers",
      "clear necessary conditions",
      "smooth trielliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}