Speaker：Sheng Rao（Wuhan University）

Time：2022-05-10, 14:30

Location：Tencent Meeting ID：157394895（Pwd：202205）

Abstract:

Inspired by a recent work of Dingchang Wei and Shengmao Zhu on the extension of closed complex differential forms and C. Voisin's usage of the $\partial\bar\partial$-lemma, we obtain several  new  theorems of deformation invariance of Hodge numbers and reprove the local stabilities of $p$-K\"ahler structures with the $\partial\bar\partial$-lemma. Our approach more concerns about the $d$-closed extension by means of the exponential operator $e^{\iota_\varphi}$. Furthermore, we prove the local stabilities of transversely $p$-K\"ahler structures with mild $\partial\bar\partial$-lemma by adapting the power series method to the foliated case, which strengthens the works of A. El Kacimi Alaoui--B. Gmira and P. Ra\'zny on the local stabilities of transversely ($1$-)K\"ahler structures. This talk is based on a joint work with Runze Zhang.