{
  "id": "math/0107142",
  "version": "v1",
  "published": "2001-07-19T23:58:42.000Z",
  "updated": "2001-07-19T23:58:42.000Z",
  "title": "Elliptic subfields and automorphisms of genus 2 function fields",
  "authors": [
    "Tony Shaska",
    "Helmut Voelklein"
  ],
  "journal": "Proceedings of Algebra, arithmetic and geometry with applications, West Lafayette, IN, 2000 (Springer, Berlin, 2004) 703--723",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We study genus 2 function fields with elliptic subfields of degree 2. The locus $\\L_2$ of these fields is a 2-dimensional subvariety of the moduli space $\\mathcal M_2$ of genus 2 fields. An equation for $\\L_2$ is already in the work of Clebsch and Bolza. We use a birational parameterization of $\\L_2$ by affine 2-space to study the relation between the j-invariants of the degree 2 elliptic subfields. This extends work of Geyer, Gaudry, Stichtenoth and others. We find a 1-dimensional family of genus 2 curves having exactly two isomorphic elliptic subfields of degree 2; this family is parameterized by the j-invariant of these subfields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-07-19T23:58:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "function fields",
      "automorphisms",
      "isomorphic elliptic subfields",
      "j-invariant",
      "extends work"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......7142S"
    }
  }
}