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arXiv · 1908.06356

Dolbeault cohomology of complex manifolds with torus action

Roman Krutowski·Taras Panov
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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 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.

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BibTeXRIS

Roman Krutowski, Taras Panov. 2019-08-18. Dolbeault cohomology of complex manifolds with torus action. https://doi.org/10.1090/conm%2F772%2F15489

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