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

TL;DR

This paper extends the classification of restrictions of reflection arrangements that are inductively free, building on recent results linking inductive freeness of arrangements and their Ziegler restrictions.

Contribution

It generalizes the classification of inductively free restrictions of reflection arrangements using a new fundamental theorem from 2024.

Findings

Extended classification of inductively free restrictions

Confirmed inductive freeness for broader class of restrictions

Utilized new theoretical link between arrangements and Ziegler restrictions

Abstract

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. In 2024, the first two authors 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 $(\mathcal A'',\kappa)$. In 2018, all reflection arrangements which admit inductively free Ziegler restrictions were classified by the first two authors. The aim of this paper is an extension of this classification to all restrictions of reflection arrangements utilizing the aforementioned fundamental result from the 2024 paper of the first two authors.