报告题目：Two transformations of complex structures: deformation and blow-up

报告简介：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.

报告人：饶胜，武汉大学数学与统计学院教授、博士生导师，2019年获批国家级人才项目，从事多复变与复几何领域的研究。相关研究成果发表在Invent. Math.,J. Math. Pures Appl., J. Algebraic Geom.,C. R. Math. Acad. Sci. Paris, Commun. Contemp. Math.,Compos. Math.,Math. Z.等国际数学杂志。

报告时间：2023年04月30日（星期日）上午9:00-11:00

报告地点：数学科学学院报告厅208

主办单位：扬州大学数学科学学院

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