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

Abstract

We give a simple proof of a result on the $\partial \bar{\partial }$-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 $\partial \bar{\partial }$-lemma property.

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

References in corpus (1)

• The Double Complex of a Blow-up

Cited by in corpus (1)

• On the deformed Bott-Chern cohomology