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arXiv · 2605.01408

Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements

Baiting Xie
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Abstract

We study the nonresonance phenomenon for complex rank-one local systems on complements of hyperplane arrangements. We refine the method of Cohen, Dimca, and Orlik and obtain a combinatorial sufficient condition for nonresonance. As an application, we strengthen a theorem of Bailet, Dimca, and Yoshinaga by removing one of its conditions. We also develop restriction and lifting techniques to prove a nonresonance theorem for line arrangements.

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Baiting Xie. 2026-05-02. Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements. https://arxiv.org/abs/2605.01408

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