Special complex structures and their deformation properties: Hodge numbers and stability

We introduce a natural map from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the infinitesimal deformations of this complex manifold. By use of this map, we generalize an extension formula in a recent work of K. Liu, X. Yang and myself. As direct corollaries, we prove several deformation invariance theorems for Hodge numbers and propose an elementrary approach to Kodaira-Spencer's local stability of Kahler structures. This talk is based on joint work with Quanting Zhao and Xueyuan Wan.​