Hyperbolicity of geometric orbifolds

TL;DR

This paper investigates complex hyperbolicity in geometric orbifolds, extending classical methods to derive degeneracy results for entire curves with ramification, even without a Second Main Theorem.

Contribution

It generalizes classical hyperbolicity techniques to geometric orbifolds, providing new degeneracy results without relying on the Second Main Theorem.

Findings

Degeneracy statements for entire curves with ramification

Extension of classical methods to orbifold setting

Results applicable where Second Main Theorem is unavailable

Abstract

We study complex hyperbolicity in the setting of geometric orbifolds introduced by F. Campana. Generalizing classical methods to this context, we obtain degeneracy statements for entire curves with ramification in situations where no Second Main Theorem is known from value distribution theory.