A uniqueness theorem for meromorphic maps into ℙⁿ with generic (2n+2) hyperplanes

2023/08/02 by Kai Zhou, Zhou, Kai
Mathematics · #32H30 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2308.01325

openalex publication_date 2023/08/02 · openalex created_date 2024/02/28 · openalex updated_date 2026/07/28

Abstract

Let H₁,…,H_2n+2 be generic (2n+2) hyperplanes in ℙⁿ. It is proved that if meromorphic maps f and g of ℂ^m into ℙⁿ satisfy f^*(H_j)=g^*(H_j) (1≤ j≤ 2n+2) and g is algebraically non-degenerate then f=g. This result is essentially implied by the proof of Hirotaka Fujimoto in papers [Nagoya Math. J., 1976(64): 117--147] and [Nagoya Math. J., 1978(71): 13--24]. This note gives a complete proof of the above uniqueness result.

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