On the cohomology of discriminantal arrangements and Orlik-Solomon algebras

Details On the cohomology of discriminantal arrangements and Orlik-Solomon algebras On the cohomology of discriminantal arrangements and Orlik-Solomon algebras

1999-03-23

arxiv.org/abs/math/9903132v1

Mathematics

Algebraic Geometry

LaTeX2e, 16 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematics

Scientific paper

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.

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