THE NON-VANISHING COHOMOLOGY OF ORLIK-SOLOMON ALGEBRAS

YUKIHITO KAWAHARA

Abstract. The cohomology on the complement of hyperplanes with the 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 and its weights with non-vanishing cohomology of Orlik-Solomon algebras, using decomposable relations arising from Latin hypercubes.