Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Arrangements – Tokyo 1998, M. Falk and H. Terao, eds. (Tokyo: Mathematical Society of Japan, 2000), 27 - 49
On the Cohomology of Discriminantal Arrangements and Orlik–Solomon Algebras
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.
First available in Project Euclid: 20 August 2018
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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