Inductive Freeness of Ziegler’s Canonical Multiderivations

Let A A be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction A'' A ′ ′ of A A to any hyperplane endowed with the natural multiplicity κ κ is then a free multiarrangement (A'',κ ) ( 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 A is inductively free, then so is the multiarrangement (A'',κ ) ( A ′ ′ , κ ) . In a related result we derive that if a deletion A' A ′ of A A is free and the corresponding restriction A'' A ′ ′ is inductively free, then so is (A'',κ ) ( A ′ ′ , κ ) —irrespective of the freeness of A A . In addition, we show counterparts of the latter kind for additive and recursive freeness.