English

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

Algebraic Geometry 2026-03-17 v2 Complex Variables

Abstract

We derive a necessary and sufficient condition on a hyperplane arrangement in Pn\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.

Keywords

Cite

@article{arxiv.2406.04069,
  title  = {Hyperbolicity of smooth logarithmic and orbifold pairs in $\mathbb{P}^n$},
  author = {Clara Dérand},
  journal= {arXiv preprint arXiv:2406.04069},
  year   = {2026}
}

Comments

ArXiV version. 32 pages, 2 figures. There was a mistake in the proof of theorem 4.7, now corrected