{
  "id": "1606.08347",
  "version": "v1",
  "published": "2016-06-27T16:19:48.000Z",
  "updated": "2016-06-27T16:19:48.000Z",
  "title": "On projectivized vector bundles and positive holomorphic sectional curvature",
  "authors": [
    "Angelynn Alvarez",
    "Gordon Heier",
    "Fangyang Zheng"
  ],
  "categories": [
    "math.DG",
    "math.AG",
    "math.CV"
  ],
  "abstract": "We generalize a construction of Hitchin to prove that, given any compact K\\\"ahler manifold $M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $E$ over $M$, the projectivized vector bundle ${\\mathbb P}(E)$ admits a K\\\"ahler metric with positive holomorphic sectional curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T16:19:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32L05",
      "32Q10",
      "32Q15",
      "53C55"
    ],
    "keywords": [
      "positive holomorphic sectional curvature",
      "projectivized vector bundle",
      "holomorphic vector bundle",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}