On extension of closed complex (basic) differential forms: Hodge numbers and (transversely) $p$-K\"ahler structures

：饶胜（武汉大学）
：2022-05-10 14:30
：

报告人：饶胜（武汉大学）

时  间：5月10日下午14:30

地  点：腾讯会议ID：157394895 (密码：202205)

内容摘要:

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.

个人简介：

饶胜，武汉大学教授，研究方向为复流形的形变理论和上同调等，研究工作发表在Invent. Math., Compos. Math., J. Algebraic Geom. ,J. Math. Pures Appl.等重要数学杂志。

 

联系人：杨波