Dolbeault cohomology of complex manifolds with torus action
Dolbeault cohomology of complex manifolds with torus action
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 a foliated analogue of toric blow-up.
15 pages, published version
Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, FOS: Mathematics, Algebraic Topology (math.AT), 32J18, 32L05, 32M05, 32Q55, 37F75, 57R19, 57S12, 14M25, Mathematics - Algebraic Topology, Complex Variables (math.CV), Algebraic Geometry (math.AG)
Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, FOS: Mathematics, Algebraic Topology (math.AT), 32J18, 32L05, 32M05, 32Q55, 37F75, 57R19, 57S12, 14M25, Mathematics - Algebraic Topology, Complex Variables (math.CV), Algebraic Geometry (math.AG)
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