{
  "id": "2312.11197",
  "version": "v2",
  "published": "2023-12-18T13:44:09.000Z",
  "updated": "2023-12-19T07:04:31.000Z",
  "title": "A boundedness theorem for principal bundles on curves",
  "authors": [
    "Huai-Liang Chang",
    "Shuai Guo",
    "Jun Li",
    "Wei-Ping Li",
    "Yang Zhou"
  ],
  "comment": "16 pages, bibliography updated",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $G$ be a reductive group acting on an affine scheme $V$. We study the set of principal $G$-bundles on a smooth projective curve $\\mathcal C$ such that the associated $V$-bundle admits a section sending the generic point of $\\mathcal C$ into the GIT stable locus $V^{\\mathrm{s}}(\\theta)$. We show that after fixing the degree of the line bundle induced by the character $\\theta$, the set of such principal $G$-bundles is bounded. The statement of our theorem is made slightly more general so that we deduce from it the boundedness for $\\epsilon$-stable quasimaps and $\\Omega$-stable LG-quasimap.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-12-19T07:04:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14N35",
      "14L17",
      "14L30"
    ],
    "keywords": [
      "principal bundles",
      "boundedness theorem",
      "smooth projective curve",
      "bundle admits",
      "affine scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}