A combinatorial sufficient condition for nonresonance of complex rank-one local systems on hyperplane arrangement complements is obtained by refining the Cohen-Dimca-Orlik method, strengthening an earlier theorem and proving a result for line arrangements via restriction and lifting.
Homology of Local Systems on Real Line Arrangement Complements
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abstract
We study the homology groups of the complement of a complexified real line arrangement with coefficients in complex rank-one local systems. Using Borel--Moore homology, we establish an algorithm computing their dimensions via the real figures of the arrangement. It enables us to give a new upper bound. We further consider the case where the arrangement contains a sharp pair and make partial progress on a conjecture proposed by Yoshinaga.
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2026 1verdicts
UNVERDICTED 1representative citing papers
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Combinatorial Nonresonance Theorems for Hyperplane Arrangement Complements
A combinatorial sufficient condition for nonresonance of complex rank-one local systems on hyperplane arrangement complements is obtained by refining the Cohen-Dimca-Orlik method, strengthening an earlier theorem and proving a result for line arrangements via restriction and lifting.