Cohomology of local sheaves on arrangement lattices
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- by Sergey Yuzvinsky PDF
- Proc. Amer. Math. Soc. 112 (1991), 1207-1217 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 1207-1217
- MSC: Primary 52B30; Secondary 05B35, 13D40, 32S20
- DOI: https://doi.org/10.1090/S0002-9939-1991-1062840-2
- MathSciNet review: 1062840