Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911660687491072 |
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| author | Xie, Baiting |
| author_facet | Xie, Baiting |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01408 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements Xie, Baiting Algebraic Geometry 32S22 (Primary) 14N20, 14J17, 14F40, 52C35 (Secondary) 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. |
| title | Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements |
| topic | Algebraic Geometry 32S22 (Primary) 14N20, 14J17, 14F40, 52C35 (Secondary) |
| url | https://arxiv.org/abs/2605.01408 |