David Eisenbud, Sorin Popescu, and Sergey Yuzvinsky
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.