Dolbeault cohomology of complex manifolds with torus action
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 momentangle manifolds, LVM and LVMBmanifolds 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 Kähler (equivalently, polytopal) case using a foliated analogue of toric blowup.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.06356
 Bibcode:
 2019arXiv190806356K
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Complex Variables;
 32J18;
 32L05;
 32M05;
 32Q55;
 37F75;
 57R19;
 14M25
 EPrint:
 15 pages, revised version