The $\partial\bar{\partial}$-lemma under surjective maps
Algebraic Geometry
2022-04-25 v2 Complex Variables
Abstract
We consider the -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 -lemma if and only if so do all its components.
Cite
@article{arxiv.1905.13585,
title = {The $\partial\bar{\partial}$-lemma under surjective maps},
author = {Lingxu Meng},
journal= {arXiv preprint arXiv:1905.13585},
year = {2022}
}
Comments
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