具有环面作用的复流形的Dolbeault上同调

Roman Krutowski, T. Panov
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引用次数: 1

摘要

描述了一类具有环面对称群的复流形上规范叶的基本Dolbeault上同调代数。该类包括复矩角流形、LVM-流形和lvmb -流形,以及具有极大全纯环面作用的复流形。我们还给出了普通Dolbeault上同代数的DGA模型。基本Dolbeault上同的Hodge分解是通过使用环面膨胀的叶状模拟来简化到横向Kähler(等效地,多向)情况来证明的。
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Dolbeault cohomology of complex manifolds with torus action
We describe the basic Dolbeault 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 Kähler (equivalently, polytopal) case using a foliated analogue of toric blow-up.
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