Inductive freeness of Ziegler's canonical multiderivations for reflection arrangements

摘要

LetAbe a free hyperplane arrangement. In 1989, Ziegler showed that the restrictionA″ofAto 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 reflection arrangements.More precisely, letA=A(W)be the reflection arrangement of a complex reflection groupW. By work of Terao, each such reflection arrangement is free. Thus so is Ziegler's canonical multiplicity on the restrictionA″ofAto a hyperplane. We show that the latter is inductively free as a multiarrangement if and only ifA″itself is inductively free.