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

TL;DR

This paper establishes a Leray-Hirsch type theorem and provides an explicit blow-up formula for Dolbeault cohomology on complex manifolds, with applications to certain classes of manifolds and cohomological properties.

Contribution

It introduces a new theorem and explicit formula for Dolbeault cohomology under blow-ups, extending previous results to non-compact complex manifolds.

Findings

Leray-Hirsch type theorem for Dolbeault cohomology

Explicit blow-up formula for complex manifolds

Applications to strongly q-complete manifolds and the ∂∂̄-lemma

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.