{
  "id": "1902.04136",
  "version": "v1",
  "published": "2019-02-11T20:35:33.000Z",
  "updated": "2019-02-11T20:35:33.000Z",
  "title": "On automorphisms of moduli spaces of parabolic vector bundles",
  "authors": [
    "Carolina Araujo",
    "Thiago Fassarella",
    "Inder Kaur",
    "Alex Massarenti"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Fix $n\\geq 5$ general points $p_1, \\dots, p_n\\in\\mathbb{P}^1$, and a weight vector $\\mathcal{A} = (a_{1}, \\dots, a_{n})$ of real numbers $0 \\leq a_{i} \\leq 1$. Consider the moduli space $\\mathcal{M}_{\\mathcal{A}}$ parametrizing rank two parabolic vector bundles with trivial determinant on $\\big(\\mathbb{P}^1, p_1,\\dots , p_n\\big)$ which are semistable with respect to $\\mathcal{A}$. Under some conditions on the weights, we determine and give a modular interpretation for the automorphism group of the moduli space $\\mathcal{M}_{\\mathcal{A}}$. It is isomorphic to $\\left(\\frac{\\mathbb{Z}}{2\\mathbb{Z}}\\right)^{k}$ for some $k\\in \\{0,\\dots, n-1\\}$, and is generated by admissible elementary transformations of parabolic vector bundles. The largest of these automorphism groups, with $k=n-1$, occurs for the central weight $\\mathcal{A}_{F}= \\left(\\frac{1}{2},\\dots,\\frac{1}{2}\\right)$. The corresponding moduli space ${\\mathcal M}_{\\mathcal{A}_F}$ is a Fano variety of dimension $n-3$, which is smooth if $n$ is odd, and has isolated singularities if $n$ is even.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T20:35:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H37",
      "14J10",
      "14J45",
      "14E30"
    ],
    "keywords": [
      "parabolic vector bundles",
      "automorphism group",
      "trivial determinant",
      "weight vector",
      "modular interpretation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}