{
  "id": "1801.08632",
  "version": "v1",
  "published": "2018-01-25T23:42:59.000Z",
  "updated": "2018-01-25T23:42:59.000Z",
  "title": "Connectedness of The Moduli Space of Artin-Schreier Curves of Fixed Genus",
  "authors": [
    "Huy Dang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the moduli space $\\mathcal{AS}_{g}$ of Artin-Schreier curves of genus $g$ over an algebraically closed field $k$ of positive characteristic $p$. The moduli space is partitioned by irreducible strata, where each stratum parameterizes Artin-Schreier curves whose ramification divisors have the same coefficients. We construct deformations of these curves to study the relations between those strata. As an application, when $p=3$, we prove that $\\mathcal{AS}_{g}$ is connected for all possible $g$. When $p>3$, it turns out that $\\mathcal{AS}_{g}$ is connected for sufficiently large value of $g$. In the course of our work, we answer Pries and Zhu's question about how a combinatorial graph determines the geometry of $\\mathcal{AS}_g$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-25T23:42:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "fixed genus",
      "stratum parameterizes artin-schreier curves",
      "connectedness",
      "combinatorial graph determines"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}