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Hyperplane arrangement cohomology and monomials in the exterior algebra


Authors: David Eisenbud, Sorin Popescu and Sergey Yuzvinsky
Journal: Trans. Amer. Math. Soc. 355 (2003), 4365-4383
MSC (2000): Primary 15A75, 52C35, 55N45; Secondary 55N99, 14Q99
DOI: https://doi.org/10.1090/S0002-9947-03-03292-6
Published electronically: July 10, 2003
MathSciNet review: 1986506
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

David Eisenbud
Affiliation: Department of Mathematics, University of California Berkeley, Berkeley, California 94720
Email: de@msri.org

Sorin Popescu
Affiliation: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794
Email: sorin@math.sunysb.edu

Sergey Yuzvinsky
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: yuz@math.uoregon.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03292-6
Received by editor(s): April 1, 2001
Published electronically: July 10, 2003
Additional Notes: The first two authors are grateful to the NSF for support during the preparation of this work. The authors would like to thank the Mathematical Sciences Research Institute in Berkeley for its support while part of this paper was being written
Article copyright: © Copyright 2003 American Mathematical Society