Geometric theory of variety of minimal rational tangents and recognition problems on G/P and their uniruled projective subvarieies

Speaker: Ngaiming MOK, The University of Hong Kong

Venue: 210 Haina Complex Building 2, Zijingang Campus

Abstract: In this lecture.I will focus on characterization problems involving VMRT's and sub-VMRTs. This includes the problem of rigidity under projective deformation of rational homogeneous spaces X= G/P of Picard number 1 (Hwang-Mok 2005). the Recognition Problem for the characterization of X = G/P by its VMRT Cx(X) c PTx(X) at a general point(Mok 2008. Hong-Hwana 2008. Hwang-Li 2021) and the problem in algebraic geometry of characterizing certain projective subvarieties of X such as smooth nonlinear Schubert cvcles Hong-Mok 2013. 2021:Mok-Zhang 2019). In addition, we give applications of our study of sub-VMRT structures to rigidity problems conceming proper holomorphic maps on the interface of several complex variables and Cauchy-Riemann geometry (Kim-Mok-Seo 2023) and to the characterizationof certain holomorphic isometric embeddings of the complex unit ball in Kähler geometry(Mok-Yang)