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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Hyperplane arrangement cohomology and monomials in the exterior algebra
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by David Eisenbud, Sorin Popescu and Sergey Yuzvinsky PDF
Trans. Amer. Math. Soc. 355 (2003), 4365-4383 Request permission

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
  • MR Author ID: 62330
  • ORCID: 0000-0002-5418-5579
  • 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
  • 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
  • © Copyright 2003 American Mathematical Society
  • 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
  • MathSciNet review: 1986506