Advanced Studies in Pure Mathematics

On the Cohomology of Discriminantal Arrangements and Orlik–Solomon Algebras

Daniel C. Cohen

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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.

Article information

Arrangements – Tokyo 1998, M. Falk and H. Terao, eds. (Tokyo: Mathematical Society of Japan, 2000), 27-49

First available in Project Euclid: 20 August 2018

Permanent link to this document euclid.aspm/1534788964

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35] 55N25: Homology with local coefficients, equivariant cohomology
Secondary: 20F36: Braid groups; Artin groups

discriminantal arrangement local system Orlik–Solomon algebra


Cohen, Daniel C. On the Cohomology of Discriminantal Arrangements and Orlik–Solomon Algebras. Arrangements – Tokyo 1998, 27--49, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02710027.

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