{
  "id": "2106.09131",
  "version": "v1",
  "published": "2021-06-16T21:05:16.000Z",
  "updated": "2021-06-16T21:05:16.000Z",
  "title": "Compactness for $Ω$-Yang-Mills connections",
  "authors": [
    "Xuemiao Chen",
    "Richard A. Wentworth"
  ],
  "comment": "28 pp",
  "categories": [
    "math.DG"
  ],
  "abstract": "On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\\Omega$-Yang-Mills connections, where $\\Omega$ is a smooth, not necessarily closed, $(n-4)$-form. Special cases include $\\Omega$-anti-self-dual connections and Hermitian-Yang-Mills connections over general complex manifolds. By a key observation, a weak compactness result is obtained for moduli space of smooth $\\Omega$-Yang-Mills connections with uniformly $L^2$ bounded curvature, and it can be improved in the case of Hermitian-Yang-Mills connections over general complex manifolds. A removable singularity theorem for singular $\\Omega$-Yang-Mills connections on a trivial bundle with small energy concentration is also proven. As an application, it is shown how to compactify the moduli space of smooth Hermitian-Yang-Mills connections on unitary bundles over a class of balanced manifolds of Hodge-Riemann type. This class includes the metrics coming from multipolarizations, and in particular, the Kaehler metrics. In the case of multipolarizations on a projective algebraic manifold, the compactification of smooth irreducible Hermitian-Yang-Mills connections with fixed determinant modulo gauge transformations inherits a complex structure from algebro-geometric considerations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-16T21:05:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C07",
      "58E15",
      "14D20"
    ],
    "keywords": [
      "hermitian-yang-mills connections",
      "general complex manifolds",
      "determinant modulo gauge transformations inherits",
      "compactness",
      "moduli space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}