Cohomology of the Orlik-Solomon algebras and local systems

Details Cohomology of the Orlik-Solomon algebras and local systems Cohomology of the Orlik-Solomon algebras and local systems

1998-06-24

arxiv.org/abs/math/9806137v1

Mathematics

Combinatorics

latex, 28 p

Scientific paper

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 classification of generalized Cartan matrices and study of pencils of algebraic curves defined by mentioned positive dimensional components.

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