Normal Families of Holomorphic Curves and Sharing of Moving Hyperplanes Wandering on $\mathbb{P}^n$

TL;DR

This paper extends normality criteria for families of holomorphic curves in projective space, focusing on the sharing of moving hyperplanes, and establishes new conditions for their normality.

Contribution

It introduces a sufficient condition for the normality of families of holomorphic curves sharing moving hyperplanes in projective space, generalizing previous results.

Findings

Established a normality criterion involving wandering moving hyperplanes.

Extended Schwick's results from one variable to higher-dimensional projective spaces.

Provided new insights into the behavior of holomorphic curves sharing hyperplanes.

Abstract

In this paper, we extend a result of Schwick concerning normality and sharing values in one complex variable for families of holomorphic curves taking values in $\mathbb{P}^n$. We consider wandering moving hyperplanes (i.e., depending on the respective holomorphic curve in the family under consideration), and establish a sufficient condition of normality concerning shared hyperplanes.