We consider the $\partial\bar{\partial}$-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 $\partial\bar{\partial}$-lemma if and only if all of its components do as well.
Lingxu MENG
. THE $\partial\bar{\partial}$-LEMMA UNDER SURJECTIVE MAPS[J]. Acta mathematica scientia, Series B, 2022
, 42(3)
: 865
-875
.
DOI: 10.1007/s10473-022-0303-9
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