{
  "id": "1810.09115",
  "version": "v1",
  "published": "2018-10-22T07:13:46.000Z",
  "updated": "2018-10-22T07:13:46.000Z",
  "title": "Automorphism groups of almost homogeneous varieties",
  "authors": [
    "Michel Brion"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is arithmetic. Along the way, we obtain a restrictive condition for $G$ to be the full automorphism group of some normal projective variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-22T07:13:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J50",
      "14L10",
      "14M17"
    ],
    "keywords": [
      "homogeneous varieties",
      "normal projective variety",
      "open dense orbit",
      "full automorphism group",
      "smooth connected algebraic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}