Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

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 or...

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Autores principales:	Angella Daniele, Suwa Tatsuo, Tardini Nicoletta, Tomassini Adriano
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2020
Materias:	complex manifold non-kähler geometry ∂ ̅∂-lemma hodge decomposition modification blowup dolbeault cohomology orbifold 32q99 32c35 32s45 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7219d42c853d4ebf8886e0602058102b
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id	oai:doaj.org-article:7219d42c853d4ebf8886e0602058102b
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spelling	oai:doaj.org-article:7219d42c853d4ebf8886e0602058102b2021-12-02T17:14:47ZNote on Dolbeault cohomology and Hodge structures up to bimeromorphisms2300-744310.1515/coma-2020-0103https://doaj.org/article/7219d42c853d4ebf8886e0602058102b2020-09-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0103https://doaj.org/toc/2300-7443We 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.Angella DanieleSuwa TatsuoTardini NicolettaTomassini AdrianoDe Gruyterarticlecomplex manifoldnon-kähler geometry∂ ̅∂-lemmahodge decompositionmodificationblowupdolbeault cohomologyorbifold32q9932c3532s45MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 194-214 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	complex manifold non-kähler geometry ∂ ̅∂-lemma hodge decomposition modification blowup dolbeault cohomology orbifold 32q99 32c35 32s45 Mathematics QA1-939
spellingShingle	complex manifold non-kähler geometry ∂ ̅∂-lemma hodge decomposition modification blowup dolbeault cohomology orbifold 32q99 32c35 32s45 Mathematics QA1-939 Angella Daniele Suwa Tatsuo Tardini Nicoletta Tomassini Adriano Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
description	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.
format	article
author	Angella Daniele Suwa Tatsuo Tardini Nicoletta Tomassini Adriano
author_facet	Angella Daniele Suwa Tatsuo Tardini Nicoletta Tomassini Adriano
author_sort	Angella Daniele
title	Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
title_short	Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
title_full	Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
title_fullStr	Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
title_full_unstemmed	Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
title_sort	note on dolbeault cohomology and hodge structures up to bimeromorphisms
publisher	De Gruyter
publishDate	2020
url	https://doaj.org/article/7219d42c853d4ebf8886e0602058102b
work_keys_str_mv	AT angelladaniele noteondolbeaultcohomologyandhodgestructuresuptobimeromorphisms AT suwatatsuo noteondolbeaultcohomologyandhodgestructuresuptobimeromorphisms AT tardininicoletta noteondolbeaultcohomologyandhodgestructuresuptobimeromorphisms AT tomassiniadriano noteondolbeaultcohomologyandhodgestructuresuptobimeromorphisms
_version_	1718381264892854272

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

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