{
  "id": "1712.06749",
  "version": "v1",
  "published": "2017-12-19T02:06:31.000Z",
  "updated": "2017-12-19T02:06:31.000Z",
  "title": "Dolbeault cohomologies of blowing up complex manifolds",
  "authors": [
    "Sheng Rao",
    "Song Yang",
    "Xiangdong Yang"
  ],
  "comment": "All comments are welcome. 23 Pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.CV",
    "math.DG"
  ],
  "abstract": "We prove a blow-up formula for Dolbeault cohomologies of compact complex manifolds. As corollaries, we present a uniform proof for bimeromorphic invariance of $(*,0)$- and $(0,*)$-Hodge numbers on a compact complex manifold and also the differences of the same-type Bott-Chern and Hodge numbers on a complex threefold, and obtain the equality for the numbers of the blow-ups and blow-downs in the weak factorization of the bimeromorphic map between two compact complex manifolds with equal $(1,1)$-Hodge number or equivalently second Betti number. Many examples of the latter one are listed. Inspired by these, we obtain the bimeromorphic stability for degeneracy of the Fr\\\"olicher spectral sequences at $E_1$ on compact complex threefolds and fourfolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-19T02:06:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32S45",
      "14E05",
      "18G40",
      "32S20",
      "14D07"
    ],
    "keywords": [
      "dolbeault cohomologies",
      "compact complex manifold",
      "hodge number",
      "compact complex threefolds",
      "equivalently second betti number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}