Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
Abstract: 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.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms ; volume:7 ; number:1 ; year:2020 ; pages:194-214 ; extent:21
Complex manifolds ; 7, Heft 1 (2020), 194-214 (gesamt 21)
- Creator
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Angella, Daniele
Suwa, Tatsuo
Tardini, Nicoletta
Tomassini, Adriano
- DOI
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10.1515/coma-2020-0103
- URN
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urn:nbn:de:101:1-2410281510361.310105567244
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:20 AM CEST
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Associated
- Angella, Daniele
- Suwa, Tatsuo
- Tardini, Nicoletta
- Tomassini, Adriano
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