Abstract

Let $\mathcal{𝒜}$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction ${\mathcal{𝒜}}^{\prime \prime }$ of $\mathcal{𝒜}$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement. Recently, Hoge and Röhrle (2025) proved an analogue of Ziegler’s theorem for the stronger notion of inductive freeness: if $\mathcal{𝒜}$ is inductively free, then so is the free multiarrangement $({\mathcal{𝒜}}^{\prime \prime },\kappa )$.

Hoge and Röhrle (2018) classified all reflection arrangements which admit inductively free Ziegler restrictions. The aim of this paper is to extend this classification to all arrangements which are induced by reflection arrangements utilizing the aforementioned fundamental result of Hoge and Röhrle (2025).

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Mathematical Subject Classification

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