# Study of some holomorphic curves in $\C^3$ and their projection into the complex projectve space $\C P^2$

## TL;DR

This paper investigates holomorphic curves in complex three-space that avoid certain hyperplanes and subspaces, demonstrating that their projections into complex projective space can be non-constant, which challenges previous assumptions.

## Contribution

It provides new insights into the behavior of holomorphic curves avoiding specific subspaces, showing their projections into projective space are not always constant.

## Key findings

- Projections of certain holomorphic curves into $ ext{CP}^2$ can be non-constant.
- Holomorphic curves avoiding four hyperplanes and a real subspace exhibit unexpected projection properties.

## Abstract

We study holomorphic curves $f:\C\longrightarrow \C^3$ avoiding four complex hyperplanes and a real subspace of real dimension four or five in $\C^3$. We show that the projection of $f$ into the complex projective space $\C P^2$ is not necessarily constant.