{
  "id": "1806.05400",
  "version": "v1",
  "published": "2018-06-14T07:40:17.000Z",
  "updated": "2018-06-14T07:40:17.000Z",
  "title": "Boundedness properties of automorphism groups of forms of flag varieties",
  "authors": [
    "Attila Guld"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $K$ be a field of characteristic $0$, containing all roots of unity. We call a flag variety admissible if the sequence of nonnegative integers $d_1<...<d_r$ corresponding to the dimensions of the linear subspaces forming an arbitrary flag of the variety is subject to the following condition. There exists an $i\\in\\{1,..,r\\}$ such that $d_i+d_{r-i+1}\\neq \\dim V$, where $V$ is the underlying vector space of the flag variety. This condition excludes an additional $\\mathbb{Z}/2\\mathbb{Z}$-symmetry of the flag variety. Let the $K$-variety $X$ be a form of an admissible flag variety. We prove that $X$ is either ruled, or the automorphism group of $X$ is bounded, meaning that, there exists a constant $C\\in\\mathbb{N}$ such that if $G$ is a finite subgroup of $Aut_K(X)$, then the cardinality of $G$ is smaller than $C$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-14T07:40:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "boundedness properties",
      "finite subgroup",
      "admissible flag variety",
      "condition excludes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}