The $\partial \bar{\partial }$-lemma under surjective maps

Abstract

We consider the $\partial \bar{\partial }$-lemma for complex manifolds under surjective holomorphic maps. Furthermore, using Deligne-Griffiths-Morgan-Sullivan's theorem, we prove that a product compact complex manifold satisfies the $\partial \bar{\partial }$-lemma if and only if so do all its components.

11 pages. The original paper is titled with "Three theorems on the $\partial \bar{\partial }$-lemma", which has been broken up into several parts. The present paper is one part of it. Other parts are divided into arXiv:1904.08561 and arXiv:2010.03102

References in corpus (6)

• The Double Complex of a Blow-up
• Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
• On the Structure of Double Complexes
• Quantitative and qualitative cohomological properties for non-Kähler manifolds
• Bott-Chern blow-up formula and bimeromorphic invariance of the $\partial \bar{\partial }$-Lemma for threefolds
• Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology