On holomorphic curves into complex projective varieties

TL;DR

This paper investigates the behavior of holomorphic curves into complex projective varieties with specific growth conditions on their derivatives, using Nevanlinna theory to analyze their properties.

Contribution

It introduces a new perspective on holomorphic curves with controlled derivative growth in the context of complex projective varieties, expanding the application of Nevanlinna theory.

Findings

Holomorphic curves with derivative bounds exhibit specific value distribution properties.

The growth condition $ orm{f'(z)}=O(|z|^\sigma)$ influences the value distribution of the curves.

Results connect derivative growth rates to geometric and value distribution characteristics.

Abstract

In this paper, we study holomorphic curves satisfying the Fubini-Study derivative $\|f'(z)\|=O(|z|^\sigma)$ for some $\sigma>-1$ from the viewpoint of Nevanlinna theory