Sui Chung Ng, East China Normal U., Shanghai

On polarization technique and Segre varieties 

Abstract

Polarization is a simple but very useful technique in Several Complex Variables and Complex Geometry. Namely, starting from an identity involving certain complex variables and their conjugates, one can obtain more identities by varying the conjugate variables independently. The resulting identities are then holomorphic in the original complex variables and are usually more powerful. The notion of Segre varieties came from polarization and they are the "polarized" real analytic varieties. In this talk, we will discuss how polarization and Segre varieties are useful in the rigidity of holomorphic mappings and Cauchy-Riemann mappings pertaining to various complex domains and CR manifolds.