Dolbeault cohomology of complex manifolds with torus action

Roman Krutowski, Taras Panov

Published 2019-08-18Version 1

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.