Published Paper
Inserted: 30 dec 2017
Last Updated: 30 apr 2021
Journal: Complex Manifolds
Volume: 7
Number: 1
Pages: 20200103
Year: 2020
Abstract:
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