Hyperplane arrangement cohomology and monomials in the exterior algebra |
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| Authors: | David Eisenbud Sorin Popescu Sergey Yuzvinsky |
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| Institution: | Department of Mathematics, University of California Berkeley, Berkeley, California 94720 ; Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794 ; Department of Mathematics, University of Oregon, Eugene, Oregon 97403 |
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| Abstract: | We show that if  is the complement of a complex hyperplane arrangement, then the homology of  has linear free resolution as a module over the exterior algebra on the first cohomology of  . We study invariants of  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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