Non-Kähler Calabi–Yau manifolds arise naturally in the process of degenerations or resolutions and they have become one of the most important players in geometry in recent years. In the talk, we will study the finite distance problem of the moduli of non-Kähler Calabi–Yau ddbar-threefolds with respect to the period-map metric via Hodge theory. I will explain how to extend C.-L. Wang’s finite distance criterion for one-parameter degenerations in this setup.

From this point of view, we find a sufficient condition for a non-Kähler Calabi–Yau to support the ddbar-lemma, which generalizes the results by R. Friedman and C. Li.