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.
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An algorithm computes homology dimensions of line arrangement complements via real figures, yielding a new upper bound and partial progress on Yoshinaga's conjecture.
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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.
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Homology of Local Systems on Real Line Arrangement Complements
An algorithm computes homology dimensions of line arrangement complements via real figures, yielding a new upper bound and partial progress on Yoshinaga's conjecture.