HYPERPLANE ARRANGEMENT COHOMOLOGY AND MONOMIALS IN THE EXTERIOR ALGEBRA

DAVID EISENBUD SORIN POPESCU SERGEY YUZVINSKY

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