{
  "id": "1305.4501",
  "version": "v1",
  "published": "2013-05-20T11:28:16.000Z",
  "updated": "2013-05-20T11:28:16.000Z",
  "title": "Bielliptic curves of genus 3 in the hyperelliptic moduli",
  "authors": [
    "T. Shaska",
    "F. Thompson"
  ],
  "journal": "Appl. Algebra Engrg. Comm. Comput. 24 (2013), no. 5, 387 -- 412",
  "doi": "10.1007/s00200-013-0209-9",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we study bielliptic curves of genus 3 defined over an algebraically closed field $k$ and the intersection of the moduli space $\\M_3^b$ of such curves with the hyperelliptic moduli $\\H_3$. Such intersection $\\S$ is an irreducible, 3-dimensional, rational algebraic variety. We determine the equation of this space in terms of the $Gl(2, k)$-invariants of binary octavics as defined in \\cite{hyp_mod_3} and find a birational parametrization of $\\S$. We also compute all possible subloci of curves for all possible automorphism group $G$. Moreover, for every rational moduli point $\\p \\in \\S$, such that $| \\Aut (\\p) | > 4$, we give explicitly a rational model of the corresponding curve over its field of moduli in terms of the $Gl(2, k)$-invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-20T11:28:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H10",
      "14H37",
      "14Q05"
    ],
    "keywords": [
      "hyperelliptic moduli",
      "rational algebraic variety",
      "study bielliptic curves",
      "rational moduli point",
      "invariants"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.4501S"
    }
  }
}