On the Freeness of 3-Arrangements

Hyperplane arrangements in a three-dimensional vector spaceare considered in this paper. A characterization of the freenessof such an arrangement is given in terms of the characteristicpolynomial and a restricted multiarrangement. As an application,the freeness of cones over certain two-dimensional affine arrangementsis proved. 2000 Mathematics Subject Classification 52C35 (primary),32S22 (secondary).