{
  "id": "math/0601168",
  "version": "v1",
  "published": "2006-01-09T08:10:47.000Z",
  "updated": "2006-01-09T08:10:47.000Z",
  "title": "Universal Families on moduli spaces of principal bundles on curves",
  "authors": [
    "V. Balaji",
    "I. Biswas",
    "D. S. Nagaraj",
    "P. E. Newstead"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $H$ be a connected semisimple linear algebraic group defined over $\\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial stable principal $H$-bundles over $X$ whose automorphism group coincides with the centre of $H$. It is a Zariski open dense subset of the moduli space of stable principal $H$-bundles. We prove that there is a universal principal $H$-bundle over $X\\times {\\mathcal M}'_X(H)$ if and only if $H$ is an adjoint group (that is, the centre of $H$ is trivial).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-01-09T08:10:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "principal bundles",
      "universal families",
      "connected semisimple linear algebraic group",
      "zariski open dense subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1168B"
    }
  }
}