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

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