Inductive Freeness of Ziegler's Canonical Multiderivations

Let $\mathcal{A}$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction ${\mathcal{A}}^{\mathrm{\prime }\mathrm{\prime }}$ of $\mathcal{A}$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement $({\mathcal{A}}^{\mathrm{\prime }\mathrm{\prime }},\kappa )$. The aim of this paper is to prove an analogue of Ziegler’s theorem for the stronger notion of inductive freeness: if $\mathcal A$isinductivelyfree,thensoisthemultiarrangement$(\mathcal A’‘,\kappa)$\mathrm{.}Inarelatedresultwederivethatifadeletion$\mathcal A’$of$\mathcal A$isfreeandthecorrespondingrestriction$\mathcal A’'$ is inductively free, then so is $({\mathcal{A}}^{\mathrm{\prime }\mathrm{\prime }},\kappa )$ – irrespective of the freeness of $\mathcal{A}$. In addition, we show counterparts of the latter kind for additive and recursive freeness.