Advanced Studies in Pure Mathematics

On the Cohomology of Discriminantal Arrangements and Orlik–Solomon Algebras

Daniel C. Cohen

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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.

Article information

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

Dates
First available in Project Euclid: 20 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534788964

Digital Object Identifier
doi:10.2969/aspm/02710027

Mathematical Reviews number (MathSciNet)
MR1796892

Zentralblatt MATH identifier
0978.32028

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

Keywords
discriminantal arrangement local system Orlik–Solomon algebra

Citation

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. https://projecteuclid.org/euclid.aspm/1534788964


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