Extension of Fujimoto's uniqueness theorems

TL;DR

This paper extends Fujimoto's uniqueness theorems for meromorphic maps, exploring cases where the maps target different projective spaces and establishing conditions under which their dimensions are equal, revealing new phenomena.

Contribution

It generalizes Fujimoto's theorems to cases with maps into different projective spaces and identifies conditions for their dimensions to coincide.

Findings

Dimensions N and n are equal under certain conditions.

New phenomena arise in the extended cases.

Extensions of Fujimoto's theorems are established.

Abstract

Hirotaka Fujimoto considered two meromorphic maps $ f $ and $ g $ of $\mathbb{C}^m $ into $\mathbb{P}^n $ such that $ f^*(H_j)=g^*(H_j)$ ($ 1\leq j\leq q $) for $ q $ hyperplanes $ H_j $ in $\mathbb{P}^n $ in general position and proved $ f=g $ under suitable conditions. This paper considers the case where $ f $ is into $\mathbb{P}^n $ and $ g $ is into $\mathbb{P}^N $ and gives extensions of some of Fujimoto's uniqueness theorems. The dimensions $ N $ and $ n $ are proved to be equal under suitable conditions. New and interesting phenomena also occur.