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Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group (1909.04075v1)
Published 9 Sep 2019 in math.AG, math.CV, and math.DG
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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