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Hyperplane Arrangement Cohomology and Monomials in the Exterior Algebra

David Eisenbud·Sorin Popescu·Sergey Yuzvinsky
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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 [2000] on resolutions of monomial ideals in the exterior algebra. We give a new conceptual proof of this result.

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David Eisenbud, Sorin Popescu, Sergey Yuzvinsky. 2001-01-02. Hyperplane Arrangement Cohomology and Monomials in the Exterior Algebra. https://arxiv.org/abs/math/9912212

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