Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology

Abstract

We prove a theorem of Leray-Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (\emph{not necessarily compact}) complex manifolds. We give applications to strongly $q$-complete manifolds and the $\partial \bar{\partial }$-lemma.

16 pages, original title "An explicit formula of blow-ups for Dolbeault cohomology", add some applications, update the references

References in corpus (2)

• The Double Complex of a Blow-up
• Morse-Novikov cohomology on complex manifolds

Cited by in corpus (3)

• Hypercohomologies of truncated twisted holomorphic de Rham complexes
• The $\partial \bar{\partial }$-lemma under surjective maps
• Holomorphic Koszul-Brylinski homology via Dolbeault cohomology