Inductive Freeness of Ziegler's Canonical Multiderivations

Abstract

Let A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A ′′ of A to any hyperplane endowed with the natural multiplicity κ is then a free multiarrangement (A ′′ , κ). The aim of this paper is to prove an analogue of Ziegler's theorem for the stronger notion of inductive freeness: if A is inductively free, then so is the multiarrangement (A ′′ , κ).In a related result we derive that if a deletion A ′ of A is free and the corresponding restriction A ′′ is inductively free, then so is (A ′′ , κ) -irrespective of the freeness of A . In addition, we show counterparts of the latter kind for additive and recursive freeness.