Some characterizations of freeness of hyperplane arrangement

Abstract

We will consider some characterizations of freeness of a hyperplane arrangement, in terms of the following properties: locally freeness, factorization of characteristic polynomial and freeness of restricted multiarrangement. In the case of 3-arrangement, freeness is characterized by factorization of characteristic polynomial and coincidence of its roots with exponents of restricted multiarrangement. In the case of higher dimension, it is characterized by a kind of locally freeness and freeness of restricted multiarrangement. As an application, we prove the freeness of certain arrangements which is conjectured by Edelman and Reiner.