English

The heredity and bimeromorphic invariance of the $\partial\overline{\partial}$-lemma property

Complex Variables 2021-08-30 v4 Differential Geometry

Abstract

We give a simple proof of a result on the ˉ\partial\bar{\partial}-lemma property under a blow-up transformation by Deligne--Griffiths--Morgan--Sullivan's criterion. Here, we use an explicit blow-up formula for Dolbeault cohomology given in our previous work, which can be induced by a morphism expressed on the level of spaces of forms and currents. At last, we discuss the heredity and bimeromorphic invariance of the ˉ\partial\bar{\partial}-lemma property.

Keywords

Cite

@article{arxiv.1904.08561,
  title  = {The heredity and bimeromorphic invariance of the $\partial\overline{\partial}$-lemma property},
  author = {Lingxu Meng},
  journal= {arXiv preprint arXiv:1904.08561},
  year   = {2021}
}

Comments

6 pages, main result was rewritten.In particular, arXiv:1905.13585 (Three theorems on the $\partial\overline{\partial}$-lemma) was divided and some results was added into the present paper