Hironaka's example

In algebraic geometry, Hironaka's example is a non-Kähler complex manifold that is a deformation of Kähler manifolds found by Heisuke Hironaka (1960, 1962). Hironaka's example can be used to show that several other plausible statements holding for smooth varieties of dimension at most 2 fail for smooth varieties of dimension at least 3.