{
  "id": "math/0609657",
  "version": "v3",
  "published": "2006-09-22T22:45:35.000Z",
  "updated": "2010-12-21T22:06:08.000Z",
  "title": "The p-rank stratification of Artin-Schreier curves",
  "authors": [
    "Rachel Pries",
    "Hui June Zhu"
  ],
  "comment": "Revisions made in Section 3 and new result added",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study a moduli space AS_g for Artin-Schreier curves of genus g over an algebraically closed field k of characteristic p. We study the stratification of AS_g by p-rank into strata AS_{g,s} of Artin-Schreier curves of genus g with p-rank exactly s. We enumerate the irreducible components of AS_{g,s} and find their dimensions. As an application, when p=2, we prove that every irreducible component of the moduli space of hyperelliptic k-curves with genus g and 2-rank s has dimension g-1+s. We also determine all pairs (p,g) for which AS_g is irreducible. Finally, we study deformations of Artin-Schreier curves with varying p-rank. Keywords: Artin-Schreier, hyperelliptic, curve, moduli, p-rank.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-21T22:06:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G15",
      "14H40",
      "14K15"
    ],
    "keywords": [
      "artin-schreier curves",
      "p-rank stratification",
      "moduli space",
      "irreducible component",
      "hyperelliptic k-curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9657P"
    }
  }
}