Hyperbolicity of smooth logarithmic and orbifold pairs in $\mathbb{P}^n$

Abstract

We derive a necessary and sufficient condition on a hyperplane arrangement in $\mathbb{P}^n$ for the associated logarithmic cotangent bundle to be ample modulo boundary. We extend this result to the orbifold setting and give some applications concerning hyperbolicity of pairs. We improve significantly the results of Darondeau-Rousseau.