题目：Two Transformations of Complex Structures: Deformation and Blow-Up

报告人：Sheng Rao (Wuhan University)

地点：Zoom会议室

时间：2020年6月25日21：30

Abstract. 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.

Time: Thursday, Jun 25, 2020 21:30(Beijing)

Join Zoom meeting. Registration links：https://zoom.us/meeting/register/tJUuceGrrTIoGNM4M4UUnRbyuLQKxGL5QmSg

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