Two transformations of complex structures: deformation and blow-up

讲座时间 Datetime:2022年6月23日，星期四，15:00-16:30

地点 Venue: 腾讯线上会议：870-538-864

主持人 Host：邵国宽

报告人 Speaker: 饶胜

单位 Affiliation: 武汉大学

报告摘要 Abstract:

We will introduce our three 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. If time is allowed, we will also introduce the joint work with I-Hsun Tsai on deformation limit and invariance of  plurigenera of Moishezon manifolds. This talk is based on many joint works.