Meromorphic mappings on Kähler manifolds weakly sharing hyperplanes in \mathbb Pⁿ(\mathbb C)

2024/05/10 by Si Duc Quang, Quang, Si Duc
Mathematics · #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.2405.06268

openalex publication_date 2024/05/10 · openalex created_date 2024/05/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the uniqueness problem for linearly nondegenerate meromorphic mappings from a Kähler manifold into \mathbb Pⁿ(\mathbb C) satisfying a condition (C_ρ) and sharing hyperplanes in general position, where the condition that two meromorphic mappings f,g have the same inverse image for some hyperplanes H is replaced by a weaker one that f^-1(H)⊂ g^-1(H). Moreover, we also give some improvements on the uniqueness problem and algebraic dependence problem of meromorphic mappings which share hyperplanes and satisfy (C_ρ) conditions for different non-negative numbers ρ.

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