{
  "id": "1703.06312",
  "version": "v1",
  "published": "2017-03-18T16:03:33.000Z",
  "updated": "2017-03-18T16:03:33.000Z",
  "title": "Construction of constant scalar curvature Kähler cone metrics",
  "authors": [
    "Julien Keller",
    "Kai Zheng"
  ],
  "comment": "46 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "Over a compact K\\\"ahler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a K\\\"ahler metric with conic singularities along a divisor. We deduce several existence results of constant scalar curvature K\\\"ahler metrics with conic singularities: existence result under small deformations of K\\\"ahler classes, existence result over a Fano manifold, existence result over certain ruled manifolds. In this last case, we consider the projectivisation of a parabolic stable holomorphic bundle. This leads us to prove that the existing Hermitian-Einstein metric on this bundle enjoys a regularity property along the divisor on the base.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-18T16:03:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "53C25",
      "32L05",
      "53C07",
      "32Q20"
    ],
    "keywords": [
      "constant scalar curvature kähler cone",
      "scalar curvature kähler cone metrics",
      "existence result",
      "conic singularities",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}