Let V be a complex vector space of dimension I. An arrangement in V is a finite set d of hyperplanes, all containing the origin. Let L = L ( d ) be the set of intersections of elements of ~r Partially order L by reverse inclusion so that L has V as its minimal element and d as its set of atoms. The poset L is a finite geometric lattice with rank function r(X)= dim V/X, XE L. Without loss of generality we assume that N H ~ , H =0 is the maximal element of L and thus L has rank I. The characteristic polynomial z(L, t) of L is defined by