{
  "id": "1411.2152",
  "version": "v1",
  "published": "2014-11-08T19:15:45.000Z",
  "updated": "2014-11-08T19:15:45.000Z",
  "title": "Genus 3 curves whose Jacobians have endomorphisms by $Q (ζ_7 +\\barζ_7 )$, II",
  "authors": [
    "J. W. Hoffman",
    "Dun Liang",
    "Zhibin Liang",
    "Ryotaro Okazaki",
    "Yukiko Sakai",
    "Haohao Wang"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "In this work we consider constructions of genus three curves $X$ such that $\\mathrm{End}(\\mathrm{Jac} (X))\\otimes Q$ contains the totally real cubic number field $Q(\\zeta _7 +\\bar{\\zeta}_7 )$. We construct explicit three-dimensional families whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when $X$ is hyperelliptic was studied in a previous work by Hoffman and Wang and some nonhyperelliptic curves were constructed in a previous paper by Hoffman, Z. Liang. Sakai and Wang.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-08T19:15:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "endomorphisms",
      "construct explicit three-dimensional families",
      "totally real cubic number field",
      "generic member"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}