Abstract
AbstractLet 𝒜 be a line arrangement in the complex projective plane ℙ2 and let M be its complement. A rank one local system 𝓛 on M is admissible if, roughly speaking, the cohomology groups Hm(M, 𝓛) can be computed directly from the cohomology algebra H*(M, ℂ). In this work, we give a sufficient condition for the admissibility of all rank one local systems on M. As a result, we obtain some properties of the characteristic variety 𝒱1(M) and the Resonance variety 𝓡1(M).
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