We present a counterexample to the conjecture by Orlik that the restriction of a free hyperplane arrangement to one of its hyperplanes is free. I. Definitions and the counterexample This note presents a counterexample to a conjecture by Orlik on hyperplane arrangements. In what follows, we give only those definitions necessary to state the conjecture and the counterexample. For more background on the theory of hyperplane arrangements, see [Or]. Let %f be a finite set of hyperplanes (subspaces

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... codimension one) passing through the origin in Rd , and for each hyperplane H in %?, let /// be the linear form in the polynomial ring S = R[xx, ... , x,f] that vanishes on H (so that /// is uniquely defined up to a scalar multiple). The module of %?-derivations Y)ex(%?) is defined to be the set of all derivations 6 : S -► S with the property that 6(Ih) is divisible by In for all H in %?. Der(^) is a module over the polynomial ring S, and and we say ^ is a free arrangement if it is a free module over S. Given any hyperplane H in %f, we define the restriction arrangement %?\n to be the arrangement within the subspace H (thinking of H as Rd~x ) whose hyperplanes are all of the intersections of hyperplanes of