Hyperplane arrangement cohomology and monomials in the exterior algebra

Abstract

We show that if X X is the complement of a complex hyperplane arrangement, then the homology of X X has linear free resolution as a module over the exterior algebra on the first cohomology of X X . We study invariants of X X that can be deduced from this resolution. A key ingredient is a result of Aramova, Avramov, and Herzog (2000) on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result.