{
  "id": "2502.09540",
  "version": "v1",
  "published": "2025-02-13T17:56:42.000Z",
  "updated": "2025-02-13T17:56:42.000Z",
  "title": "The $p$-rank stratification of the moduli space of double covers of a fixed elliptic curve",
  "authors": [
    "Kevin Chang",
    "Dušan Dragutinović",
    "Steven R. Groen",
    "Yuxin Lin",
    "Natalia Pacheco-Tallaj",
    "Deepesh Singhal"
  ],
  "comment": "34 pages. Comments are welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper we investigate the $p$-rank stratification of the moduli space of curves of genus $g$ that admit a double cover to a fixed elliptic curve $E$ in characteristic $p>2$. We show that the closed $p$-rank strata of this moduli space are equidimensional of the expected dimension. We also show the existence of a smooth double cover of $E$ of all the possible values of the $p$-rank on this moduli space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-13T17:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14G17",
      "14H30",
      "14H40"
    ],
    "keywords": [
      "moduli space",
      "fixed elliptic curve",
      "rank stratification",
      "rank strata",
      "smooth double cover"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}