Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
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DOI：
10.1515/coma-2020-0103
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发表时间：
2017-12
影响因子：
0.5
通讯作者：
Daniele Angella;T. Suwa;Nicoletta Tardini;A. Tomassini
中科院分区：
文献类型：
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作者：
Daniele Angella;T. Suwa;Nicoletta Tardini;A. Tomassini
本文构造了一个满足Kähler-引理的单连通紧致复非Kähler流形，并赋予其一个平衡度量。为此目的，我们最初的目的是研究在紧致复流形和orbifolds的修改下，满足的性质的稳定性。这个问题最近已经在[34，39，40，50]中用不同的技术得到了解决和回答。在这里，我们提供了一个不同的方法，使用Čech上同调理论来研究的Dolbeault上同调的爆破的沿着子流形Z的紧致复流形X XZ，允许一个全纯可收缩的邻域。
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.