{
  "id": "1304.3682",
  "version": "v4",
  "published": "2013-04-12T16:55:29.000Z",
  "updated": "2013-09-24T09:43:15.000Z",
  "title": "A properness result for degenerate Quadratic and Symplectic Bundles on a smooth projective curve",
  "authors": [
    "Yashonidhi Pandey"
  ],
  "comment": "44 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $(V,q)$ be a vector bundle on a smooth projective curve $X$ together with a quadratic form $q: \\mathrm{Sym}^2(V) \\ra \\mathcal{O}_X$ (respectively symplectic form $q: \\Lambda^2V \\ra \\mathcal{O}_X$). Fixing the degeneracy locus of the quadratic form induced on $V/\\ker(q)$, we construct a coarse moduli of such objects. Further, we prove semi-stable reduction theorem for equivalence classes of such objects. In particular, the case when degeneracies of $q$ are higher than one is that of principal interest. We also provide a proof of properness of polystable orthogonal bundles without appealing to Bruhat-Tits theory in any characteristic.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-09-24T09:43:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14D23",
      "14D20"
    ],
    "keywords": [
      "smooth projective curve",
      "properness result",
      "symplectic bundles",
      "degenerate quadratic",
      "quadratic form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.3682P"
    }
  }
}