{
  "id": "1111.2819",
  "version": "v1",
  "published": "2011-11-11T19:08:49.000Z",
  "updated": "2011-11-11T19:08:49.000Z",
  "title": "Limits of balanced metrics on vector bundles and polarised manifolds",
  "authors": [
    "Mario Garcia-Fernandez",
    "Julius Ross"
  ],
  "comment": "31 pages",
  "categories": [
    "math.DG",
    "hep-th",
    "math.AG"
  ],
  "abstract": "We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter \\alpha, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of \\alpha, we prove that the limit of a convergent sequence of balanced metrics leads to a Hermitian-Einstein metric on E and a constant scalar curvature K\\\"ahler metric in c_1(L). For special values of \\alpha, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian-Einstein metric on E and a K\\\"ahler metric in c_1(L). For this, we compute the top two terms of the density of states expansion of the Bergman kernel of E \\otimes L^k.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-11T19:08:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "balanced metrics",
      "polarised manifolds",
      "hermitian-einstein metric",
      "ample line bundle",
      "holomorphic vector bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 945530,
      "adsabs": "2011arXiv1111.2819G"
    }
  }
}