Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements
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. Recently, in [HogeRöhrle2022], 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 [HogeRöhrle2018], 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 [HogeRöhrle2022].
 Publication:

arXiv eprints
 Pub Date:
 October 2022
 DOI:
 10.48550/arXiv.2210.00436
 arXiv:
 arXiv:2210.00436
 Bibcode:
 2022arXiv221000436H
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Group Theory;
 52C35;
 14N20;
 32S22;
 51D20
 EPrint:
 v1 21 pages. arXiv admin note: text overlap with arXiv:1705.02767, arXiv:2204.09540