  In this paper, we recover the characteristic polynomial of an arrangement of
hyperplanes by computing the rational equivalence class of the variety defined
by the logarithmic ideal of the arrangement. The logarithmic ideal was
introduced in [arXiv:0907.0896v2] in a study of the critical points of the
master function. The above result is used to understand the asymptotic behavior
the Hilbert series of the logarithmic ideal. As an application, we prove the
Solomon-Terao formula under the tame hypothesis by identifying each side of the
formula with a certain specialization of the Hilbert series of the logarithmic
ideal.
