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1 results

  • Cohomology of the Orlik–Solomon Algebras and Local Systems

  • Anatoly Libgober, Sergey Yuzvinsky
  • Journal:
    Compositio Mathematica / Volume 121 / Issue 3 / May 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 337-361
    Print publication:
    May 2000
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  • The paper provides a combinatorial method to decide when the space of local systems with nonvanishing 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 classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.