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arXiv · 2405.06268

Meromorphic mappings on K\"{a}hler manifolds weakly sharing hyperplanes in $\mathbb P^n(\mathbb C)$

Si Duc Quang
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Abstract

In this paper, we study the uniqueness problem for linearly nondegenerate meromorphic mappings from a K\"{a}hler manifold into $\mathbb P^n(\mathbb C)$ satisfying a condition $(C_\rho)$ 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 $f^{-1}(H)\subset g^{-1}(H)$. Moreover, we also give some improvements on the uniqueness problem and algebraic dependence problem of meromorphic mappings which share hyperplanes and satisfy $(C_\rho)$ conditions for different non-negative numbers $\rho$.

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Si Duc Quang. 2024-05-10. Meromorphic mappings on K\"{a}hler manifolds weakly sharing hyperplanes in $\mathbb P^n(\mathbb C)$. https://doi.org/10.5486/pmd.2025.9966

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