{
  "id": "1110.5620",
  "version": "v1",
  "published": "2011-10-25T19:30:54.000Z",
  "updated": "2011-10-25T19:30:54.000Z",
  "title": "Balanced Metrics and Chow Stability of Projective Bundles over Kähler Manifolds II",
  "authors": [
    "Reza Seyyedali"
  ],
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "In the previous article (\\cite{S}), we proved that slope stability of a holomorphic vector bundle $E$ over a polarized manifold $(X,L)$ implies Chow stability of $(\\mathbb{P}E^*,\\mathcal{O}_{\\mathbb{P}E^*}(1)\\otimes \\pi^* L^k)$ for $k \\gg 0$ if the base manifold has no nontrivial holomorphic vector field and admits a constant scalar curvature metric in the class of $2\\pi c_{1}(L)$. In this article using asymptotic expansions of Bergman kernel on $\\textrm{Sym}^d E$, we generalize the main theorem of \\cite{S} to polarizations $(\\mathbb{P}E^*,\\mathcal{O}_{\\mathbb{P}E^*}(d)\\otimes \\pi^* L^k)$ for $k \\gg 0$, where $d$ is a positive integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-25T19:30:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kähler manifolds",
      "projective bundles",
      "balanced metrics",
      "nontrivial holomorphic vector field",
      "constant scalar curvature metric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.5620S"
    }
  }
}