Corpus ID: 201070649

Dolbeault cohomology of complex manifolds with torus action

@article{Krutowski2019DolbeaultCO,
  title={Dolbeault cohomology of complex manifolds with torus action},
  author={Roman Krutowski and Taras E. Panov},
  journal={arXiv: Differential Geometry},
  year={2019}
}
  • Roman Krutowski, Taras E. Panov
  • Published 2019
  • Mathematics
  • arXiv: Differential Geometry
  • 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… CONTINUE READING

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