Cohomology of the Orlik-Solomon algebras and local systems

@inproceedings{Libgober2007CohomologyOT,
  title={Cohomology of the Orlik-Solomon algebras and local systems},
  author={Anatoly Libgober and Sergey Yuzvinsky},
  year={2007}
}
The paper provides a combinatorial method to decide when the space of local systems with non vanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of positive dimension. Partial classification of arrangements having such a component of positive dimension and a comparison theorem for cohomology of Orlik-Solomon algebra and cohomology of local systems are given. The methods are based on Vinberg-Kac… CONTINUE READING
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