The Non-vanishing Cohomology of Orlik-Solomon Algebras

Abstract

The cohomology of the complement of hyperplanes with coefficients in the rank one local system associated to a generic weight vanishes except in the highest dimension. In this paper, we construct matroids or arrangements admitting weights for which the Orlik-Solomon algebra has non-vanishing cohomology, using decomposable relations arising from Latin hypercubes.