Hyperplane arrangement cohomology and monomials in the exterior algebra

Eisenbud, David; Popescu, Sorin; Yuzvinsky, Sergey

doi:10.1090/S0002-9947-03-03292-6

Hyperplane arrangement cohomology and monomials in the exterior algebra
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by David Eisenbud, Sorin Popescu and Sergey Yuzvinsky

Trans. Amer. Math. Soc. 355 (2003), 4365-4383

DOI: https://doi.org/10.1090/S0002-9947-03-03292-6

Published electronically: July 10, 2003

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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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