English

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

Algebraic Geometry 2022-04-25 v2 Complex Variables

Abstract

We consider the ˉ\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 ˉ\partial\bar{\partial}-lemma if and only if so do all its components.

Keywords

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

R2 v1 2026-06-23T09:35:12.251Z