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Free and locally free arrangements with a given intersection lattice

Author: Sergey Yuzvinsky
Journal: Proc. Amer. Math. Soc. 118 (1993), 745-752
MSC: Primary 52B30; Secondary 05B35, 06A09, 32S20
MathSciNet review: 1160307
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Abstract: In previous papers the author characterized free arrangements of hyperplanes by the vanishing of cohomology of the intersection lattice with coefficients in a certain sheaf of graded modules over a polynomial ring. The main result of this paper is that for a locally free arrangement the degrees of nonzero homogeneous components of the cohomology modules are bounded by a number depending only on the intersection lattice. In particular, the Hilbert coefficients of the module of derivations of a locally free arrangement are combinatorial invariants. Another result of the paper asserts that the set of free arrangements is Zariski open in the set of all arrangements with a given intersection lattice.

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Article copyright: © Copyright 1993 American Mathematical Society

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