TL;DR
This paper investigates the cohomological properties of complex manifolds with the rational homology of a product of spheres, extending known vanishing results and exploring spectral sequence degeneration in non-Kähler contexts.
Contribution
It extends vanishing properties of bundle cohomology on homological Hopf manifolds and examines Hodge-de Rham spectral sequence degeneration in non-Kähler settings.
Findings
Extended vanishing properties of cohomology on these manifolds
Analyzed spectral sequence degeneration in non-Kähler manifolds
Included examples from Hopf, Kodaira, and Brieskorn-van de Ven constructions
Abstract
We discuss the properties of complex manifolds having rational homology of including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of bundles on such manifolds.As an application we consider degeneration of Hodge-deRham spectral sequence in this non Kahler setting.
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