Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Angella - T. Suwa - N. Tardini - A. Tomassini

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

created by daniele on 30 Dec 2017


Submitted Paper

Inserted: 30 dec 2017
Last Updated: 30 dec 2017

Year: 2017

ArXiv: 1712.08889 PDF


We investigate the stability of the property of satisfying the $\partial\overline\partial$-Lemma under modifications of compact complex manifolds. More precisely, we study the Dolbeault cohomology of the blowing-up $\tilde X_Z$ of a compact complex manifold $X$ along a submanifold $Z$ admitting a holomorphically contractible neighbourhood, and we prove that $\tilde X$ satisfies the $\partial\overline\partial$-Lemma if both $X$ and $Z$ do. We use \v{C}ech cohomology theory. Similar results have been recently proven in \cite{rao-yang-yang, yang-yang} with different techniques. By considering the orbifold case and resolutions, we provide new examples of compact complex manifolds satisfying the $\partial\overline\partial$-Lemma.

Tags: SIR2014-AnHyC

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