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arXiv · 1909.04075

Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group

Nikita Klemyatin
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Abstract

Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result to compute the Dolbeault cohomology of Vaisman manifolds.

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Nikita Klemyatin. 2019-09-09. Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group. https://doi.org/10.1016/j.geomphys.2020.103823

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