Brody curves omitting hyperplanes

TL;DR

This paper proves that Brody curves avoiding n hyperplanes in general position in complex projective space have growth order at most one, extending previous results from the case n=1 to higher dimensions.

Contribution

It generalizes the known result for n=1 to all n, establishing an upper bound on the growth order of Brody curves omitting hyperplanes.

Findings

Brody curves omitting hyperplanes have growth order at most one

The result extends Clunie and Hayman's theorem from n=1 to higher dimensions

Brody curves in this setting are shown to have normal type

Abstract

A Brody curve, a.k.a. normal curve, is a holomorphic map from the complex line to the complex projective space of dimension n, such that the family of its translations is normal. We prove that Brody curves omitting n hyperplanes in general position have growth order at most one, normal type. This generalizes a result of Clunie and Hayman who proved it for n=1.