Quasi-positive orbifold cotangent bundles ; Pushing further an example by Junjiro Noguchi

TL;DR

This paper explores the positivity properties of orbifold cotangent bundles in projective spaces, extending Noguchi's example and deriving new hyperbolicity results using modern algebraic geometry techniques.

Contribution

It advances the understanding of orbifold cotangent bundles' positivity by extending Noguchi's example with explicit global differentials and Fermat covers, leading to new hyperbolicity results.

Findings

Extended Noguchi's example significantly

Produced explicit global symmetric differentials

Derived new orbifold hyperbolicity results

Abstract

In this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category. As an application of our results, we derive two new orbifold hyperbolicity results, going beyond some classical results of value distribution theory.