Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements

Torsten Hoge, Gerhard Roehrle, Sven Wiesner

Published 2022-10-02Version 1

Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A''$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement. Recently, in [Hoge-R\"ohrle2022], an analogue of Ziegler's theorem for the stronger notion of inductive freeness was proved: if $\mathcal A$ is inductively free, then so is the free multiarrangement $(\mathcal A'',\kappa)$. In [Hoge-R\"ohrle2018], all reflection arrangements which admit inductively free Ziegler restrictions are classified. The aim of this paper is an extension of this classification to all restrictions of reflection arrangements utilizing the aforementioned fundamental result from [Hoge-R\"ohrle2022].