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<p>We derive a necessary and sufficient condition on a hyperplane arrangement in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {P}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> 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 and Rousseau (Épijournal de Géométrie Algébrique, 8 2024).</p>

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

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Clara Dérand

摘要

We derive a necessary and sufficient condition on a hyperplane arrangement in \(\mathbb {P}^n\) 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 and Rousseau (Épijournal de Géométrie Algébrique, 8 2024).