2017/12/31 by Daniele Angella, Tatsuo Suwa, Nicoletta Tardini +2 · 22 citations
Mathematics · #Algebraic Geometry and Number Theory #Cohomology #Complex manifold #Contractible space #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic function #Lemma (botany) #Manifold (fluid mechanics) #Mathematics #Pure mathematics #Submanifold #math.AT #math.CV #math.DG #msc:32C35 #msc:32Q99 #msc:32S45
paper · pdf · doi:10.1515/coma-2020-0103
published in Complex Manifolds 7(1), 194-214 (De Gruyter Open)
arxiv created 2020/08/18 · openalex publication_date 2020/09/01 · arxiv updated 2020/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ̃ X Z of a compact complex manifold X along a submanifold Z admitting a holomorphically contractible neighbourhood.