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Cohomology of local sheaves on arrangement lattices
Proceedings of the American Mathematical Society
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 adoi:10.1090/s0002-9939-1991-1062840-2 fatcat:mk2kiujygra6jfewe2l4erpm4i