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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Cohomology of local sheaves on arrangement lattices


Author: Sergey Yuzvinsky
Journal: Proc. Amer. Math. Soc. 112 (1991), 1207-1217
MSC: Primary 52B30; Secondary 05B35, 13D40, 32S20
MathSciNet review: 1062840
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Abstract: We apply cohomology of sheaves to arrangements of hyperplanes. In particular we prove an inequality for the depth of cohomology modules of local sheaves on the intersection lattice of an arrangement. This generalizes a result of Solomon-Terao about the cummulative property of local functors. We also prove a characterization of free arrangements by certain properties of the cohomlogy of a sheaf of derivation modules. This gives a condition on the Möbius function of the intersection lattice of a free arrangement. Using this condition we prove that certain geometric lattices cannot afford free arrangements although their Poincaré polynomials factor.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062840-2
PII: S 0002-9939(1991)1062840-2
Article copyright: © Copyright 1991 American Mathematical Society