Sui Chung Ng, East China Normal U., Shanghai
On polarization technique and Segre varieties
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.