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VOL. 27 | 2000 On the Cohomology of Discriminantal Arrangements and Orlik–Solomon Algebras

Abstract

We relate the cohomology of the Orlik–Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik–Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in an arbitrary complex rank one local system. We also establish the relationship between the cohomology support loci of the complement of a discriminantal arrangement and the resonant varieties of its Orlik–Solomon algebra.

Information

Published: 1 January 2000
First available in Project Euclid: 20 August 2018

zbMATH: 0978.32028
MathSciNet: MR1796892

Digital Object Identifier: 10.2969/aspm/02710027

Subjects:
Primary: 32S22, 55N25
Secondary: 20F36

Rights: Copyright © 2000 Mathematical Society of Japan

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