複素双曲多様体上の正則写像の剛性について

志賀　啓成

99.6.1, 数学教室談話会

Let $N=B^{n}/\Gamma$ be a complex hyperbolic manifold of divergence type and M a complex manifold which may not be compact nor complex hyperbolic. In this talk, we shall consider the (strong) rigidity for non-constant holomorphic maps of N to M. Generally, the rigidity does not hold. Hence, we shall consider sufficient conditions for the manifold M to have the rigidity. As an application, we shall establish a finiteness theorem for holomorphic maps of N to M if $\Gamma$ is finitely generated and if M is compact.

Also, we shall construct examples of the manifold M with the rigidity for holomorphic mappings of N and consider related topics.