{
  "id": "1809.07277",
  "version": "v1",
  "published": "2018-09-19T16:17:09.000Z",
  "updated": "2018-09-19T16:17:09.000Z",
  "title": "Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case",
  "authors": [
    "Sheng Rao",
    "Song Yang",
    "Xiangdong Yang"
  ],
  "comment": "All comments are welcome. 36 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.CV",
    "math.DG"
  ],
  "abstract": "We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Green-Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-19T16:17:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S45",
      "14E05",
      "18G40",
      "14D07"
    ],
    "keywords": [
      "bundle-valued case",
      "holomorphic vector bundle",
      "compact complex manifold",
      "dolbeault cohomology groups",
      "blow-up formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}