Sui Chung Ng, Temple U., USA

Holomorphic double fibration and the mapping problems of classical domains

Abstract

The rigidity or classification of special mappings among domains on complex manifolds is a traditional subject in Several Complex Variables. The proper holomorphic mappings between complex unit balls are among those who have attracted most attention and there have been various inputs from Algebraic Geometry, CR Geometry, PDE, etc. In this talk, we are going to look at the case of higher-rank Type-I irreducible bounded symmetric domains which remains rather unexplored comparing to the case of unit balls. We will try to illustrate some interesting linkages between the mapping problems of Type-I domains and those of generalized balls. This is by considering a very simple and natural holomorphic double fibration structure on certain flag varieties.