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

We first established a hyperplane restriction theorem for the local holomorphic mappings 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 prope...

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Bibliographic Details
Published in:Mathematische annalen 2024-01, Vol.388 (3), p.3169-3182
Main Authors: Gao, Yun, Ng, Sui-Chung
Format: Article
Language:English
Subjects:
Existence theorems
Hyperplanes
Linear systems
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:We first established a hyperplane restriction theorem for the local holomorphic mappings 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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-023-02604-y