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Admissibility of Local Systems for some Classes of Line Arrangements

  • Nguyen Tat Thang (a1)
Abstract

Let 𝒜 be a line arrangement in the complex projective plane 2 and let M be its complement. A rank one local system 𝓛 on M is admissible if, roughly speaking, the cohomology groups H m(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 𝒱 1(M) and the Resonance variety 𝓡 1(M).

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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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