{
  "id": "math/0511726",
  "version": "v1",
  "published": "2005-11-30T02:57:41.000Z",
  "updated": "2005-11-30T02:57:41.000Z",
  "title": "Elliptic curves and birational representation of Weyl groups",
  "authors": [
    "Eguchi Mitsuaki",
    "Tomoyuki Takenawa"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Some Weyl group acts on a family of rational varieties obtained by successive blow-ups at $m$ ($m\\geq n+2$) points in the projective space $\\mpp^n(\\mc)$. In this paper we study the case where all the points of blow-ups lie on a certain elliptic curve in $\\mpp^n$. Investigating the action of Weyl group on the Picard groups on the elliptic curve and on rational varieties, we show that the action on the parameters can be written as a group of linear transformations on the $(m+1)$-st power of a torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-11-30T02:57:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E07",
      "14H52",
      "14H70"
    ],
    "keywords": [
      "elliptic curve",
      "birational representation",
      "rational varieties",
      "weyl group acts",
      "blow-ups lie"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11726M"
    }
  }
}