{
  "id": "1908.06356",
  "version": "v1",
  "published": "2019-08-18T01:03:31.000Z",
  "updated": "2019-08-18T01:03:31.000Z",
  "title": "Dolbeault cohomology of complex manifolds with torus action",
  "authors": [
    "Roman Krutowski",
    "Taras Panov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.DG",
    "math.AG",
    "math.AT",
    "math.CV"
  ],
  "abstract": "We describe the basic Dolbealut cohomology algebra of the canonical foliation on a class of complex manifolds with a torus symmetry group. This class includes complex moment-angle manifolds, LVM and LVMB-manifolds and, in most generality, complex manifolds with a maximal holomorphic torus action. We also provide a dga model for the ordinary Dolbeault cohomology algebra. The Hodge decomposition for the basic Dolbeault cohomology is proved by reducing to the transversely Kaehler (equivalently, polytopal) case using an analogoue of the construction of toric blow-up.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-18T01:03:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex manifolds",
      "ordinary dolbeault cohomology algebra",
      "maximal holomorphic torus action",
      "basic dolbealut cohomology algebra",
      "complex moment-angle manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}