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BY 4.0 license Open Access Published by De Gruyter Open Access September 1, 2020

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

  • Daniele Angella EMAIL logo , Tatsuo Suwa , Nicoletta Tardini and Adriano Tomassini
From the journal Complex Manifolds


We construct a simply-connected compact complex non-Kähler manifold satisfying the ∂ ̅∂ -Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the stability of the property of satisfying the ∂ ̅∂-Lemma under modifications of compact complex manifolds and orbifolds. This question has been recently addressed and answered in [34, 39, 40, 50] with different techniques. Here, we provide a different approach using Čech cohomology theory to study the Dolbeault cohomology of the blowup ̃XZ of a compact complex manifold X along a submanifold Z admitting a holomorphically contractible neighbourhood.

MSC 2010: 32Q99; 32C35; 32S45


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Received: 2020-07-16
Accepted: 2020-08-17
Published Online: 2020-09-01

© 2020 Daniele Angella et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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