Hyperplane arrangement cohomology and monomials in the exterior algebra

@article{Eisenbud1999HyperplaneAC,
  title={Hyperplane arrangement cohomology and monomials in the exterior algebra},
  author={David Eisenbud and Sorin Popescu and Sergey Yuzvinsky},
  journal={Transactions of the American Mathematical Society},
  year={1999},
  volume={355},
  pages={4365-4383}
}
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 (2000) on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result. 
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