Abstract：We will introduce a hyperplane restriction theorem for the local holomorphic mappings between projective spaces, which is inspired by an analogous theorem of M. Green for the linear systems in projective spaces. This theorem provides us a formula to estimate the dimension of the linear span of image from that of a general linear subspace. We will apply this theorem to study the structure of rational proper mappings between complex unit balls, with a specific focus on the Gap conjecture proposed by Huang - Ji - Yin. The Huang-Ji-Yin Gap conjecture posits the existence of a sequence of gaps for the rational proper maps between complex unit balls. It is a joint work with Sui-Chung Ng.
The speaker is an associate professor at Shanghai Jiao Tong University, Her interests include algebraic geometry and several complex variables, esprcially bundles and rigidity problems about holomorphic maps.
