中科院数学与系统科学研究院
数学研究所
代数几何研讨班
报告人：高 云 教授（上海交通大学）
题 目：Dimension estimate, orthogonal maps and CR maps
时 间：2021.04.16（星期五），13:30-14:30
地 点：数学院晨兴410
摘 要：In this talk, we will introduce a dimension formula for local holomorphic mappings which is inspired from Green hyperplane restriction Theorem. This formula gives a dimension estimate for the linear spans of the images of linear subspaces. As an application, we use this formula to study the holomorphic mappings between real hyperquadrics, which is a very classical topic in Several Complex Variables. Combining the dimension formula and a notion of orthogonality, we will present a new coordinate-free approach to the study of holomorphic mappings. Using these method, we are able generalize many well-known rigidity theorems for the holomorphic mappings between the hyperquadrics, especially the degenerated cases. In addition, we will talk about Huang-Ji-Yin Conjecture on the gap phenomenon for the complex unit balls and extend it to all generalized balls. This is a joint work with Sui-Chung Ng.
附件：