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

Nikita Klemyatin

doi:10.1016/j.geomphys.2020.103823

paper

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

arXiv:1909.04075 · doi:10.1016/j.geomphys.2020.103823

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.

16 pages