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 -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 -lemma property.
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