Inductive freeness of Ziegler’s canonical multiderivations for reflection arrangements

Abstract

Let A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A 00 of A to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger freeness property of inductive freeness for these canonical free multiarrangements and investigate them for the underlying class of re ection arrangements. More precisely, let A = A (W) be the re ection arrangement of a complex re ection group W. By work of Terao, each such re ection arrangement is free. Thus so is Ziegler's canonical multiplicity on the restriction A 00 of A to a hyperplane. We show that the latter is inductively free as a multiarrangement if and only if A 00 itself is inductively free.