Under mild assumptions on the central fiber, the limit of Kähler manifolds under holomorphic deformation is Kähler.
Deformation limit and bimeromorphic embedding of Moishezo n manifolds, Commun
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The limits of Kahler manifolds under holomorphic deformations
Under mild assumptions on the central fiber, the limit of Kähler manifolds under holomorphic deformation is Kähler.