Some examples due to H. Hironaka
arXiv:1501.01129
Abstract
The aim of this paper is to explain the construction by H. Hironaka [H.61] of a holomorphic (in fact "algebraic") family of compact complex manifolds parametrized by $\C$ such for all $s \in \C\setminus \{0\}$ the fiber is projective, but such that the fiber at the origin in non k{ä}hlerian, to mathematicians which are not algebraic geometers. We also explain why it is not possible to make in the same way such an example with fiber at a simpler example of non k{ä}hlerian Moishezon manifold which is also due to H. Hironaka (see section 5).
Some more explanations and comments added