{
  "id": "1412.7738",
  "version": "v1",
  "published": "2014-12-24T19:19:13.000Z",
  "updated": "2014-12-24T19:19:13.000Z",
  "title": "Yang-Mills-Higgs connections on Calabi-Yau manifolds",
  "authors": [
    "Indranil Biswas",
    "Ugo Bruzzo",
    "Alessio Lo Giudice"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG",
    "math.DG"
  ],
  "abstract": "Let $X$ be a compact connected K\\\"ahler--Einstein manifold with $c_1(TX)\\, \\geq\\, 0$. If there is a polystable Higgs vector bundle $(E\\,,\\theta)$ on $X$ with $\\theta\\,\\not=\\, 0$, then we show that $c_1(TX)\\,=\\,0$; any $X$ satisfying this condition is called a Calabi-Yau manifold, and it admits a Ricci-flat K\\\"ahler form \\cite{Ya}. Let $(E\\,,\\theta)$ be a polystable Higgs vector bundle on a compact Ricci-flat K\\\"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang-Mills-Higgs equation for $(E\\,,\\theta)$. We prove that $h$ also satisfies the Yang-Mills-Higgs equation for $(E\\,,0)$. A similar result is proved for Hermitian structures on principal Higgs bundles on $X$ satisfying the Yang-Mills-Higgs equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-24T19:19:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J32",
      "53C07",
      "58E15"
    ],
    "keywords": [
      "calabi-yau manifold",
      "yang-mills-higgs connections",
      "polystable higgs vector bundle",
      "yang-mills-higgs equation",
      "hermitian structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1335884,
      "adsabs": "2014arXiv1412.7738B"
    }
  }
}