{
  "id": "1205.6409",
  "version": "v2",
  "published": "2012-05-29T16:21:13.000Z",
  "updated": "2012-05-31T21:09:40.000Z",
  "title": "Curves which cannot be defined over an extension of degree at most two over the field of moduli",
  "authors": [
    "Ruben A. Hidalgo",
    "Yolanda Fuertes"
  ],
  "comment": "This paper has been withdrawn by the author due to a crucial error in the provided example",
  "categories": [
    "math.AG",
    "math.CV"
  ],
  "abstract": "It has been conjectured that every algebraic curve may be defined either over its field of moduli or over an extension of degree two of it. In this paper we provide a negative answer to it by giving examples of hyperelliptic curves which cannot be defined over an extension of degree at least two over their fields of moduli.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-05-31T21:09:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H37",
      "14H45",
      "30F10"
    ],
    "keywords": [
      "algebraic curve",
      "hyperelliptic curves",
      "negative answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.6409H"
    }
  }
}