A hyperplane restriction theorem for holomorphic mappings and its application for the gap conjecture

摘要

We first established a hyperplane restriction theorem for the local holomorphic map-pings between projective spaces, which is inspired by an analogous theorem of M. Green for the linear systems on P-n. The theorem would then be used to prove the existence of a sequence of gaps for the rational proper maps between complex unit balls, conjectured by Huang-Ji-Yin. Our proof does not distinguish the unit balls from other generalized balls and thus it simultaneously demonstrates the same phenomenon for all generalized balls.

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