报告题目：Two Transformations of Complex Structures: Deformation and Blow-up

主 讲 人：饶 胜

单 位：武汉大学

时 间：7月3日15:30

地 点：数学院二楼会议室

ZOOM ID：210 089 8623

密 码：123456

摘 要：

We will introduce our recent works on two transformations of complex structures: deformation and blow-up. We prove that the p-Kahler structure with the so-called mild ddbar-lemma is stable under small differentiable deformation. This solves a problem of Kodaira in his classic and generalizes Kodaira-Spencer's local stability theorem of Kahler structure. Using a differential geometric method, we solve a logarithmic dbar-equation on Kahler manifold to revisit Deligne's degeneracy theorem for the logarithmic Hodge to de Rham spectral sequence at E1-level and Katzarkov-Kontsevich-Pantev's unobstructedness of the deformations of a log Calabi-Yau pair. Finally, we will introduce a blow-up formula for Dolbeault cohomologies of compact complex manifolds by introducing relative Dolbeault cohomology. This talk is based on several joint works with Kefeng Liu, Xueyuan Wan, Song Yang, Xiangdong Yang, Quanting Zhao, etc.

简 介：

饶胜，武汉大学教授，2019年国家优青，研究方向为复几何。饶胜教授与刘克峰教授等合作者在复几何领域多个研究方向得到重要的原创性成果。相关论文发表在Invent.Math，Journal of algebraic geometry，JMPA，Compositio Math等著名杂志。