# 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} }

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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