Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements
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| Format: | Preprint |
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2022
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| _version_ | 1866917921014415360 |
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| author | Hoge, Torsten Roehrle, Gerhard Wiesner, Sven |
| author_facet | Hoge, Torsten Roehrle, Gerhard Wiesner, Sven |
| contents | 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 $κ$ 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 $(\mathcal A'',κ)$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2210_00436 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements Hoge, Torsten Roehrle, Gerhard Wiesner, Sven Combinatorics Group Theory 52C35, 14N20, 32S22, 51D20 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 $κ$ 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 $(\mathcal A'',κ)$. 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. |
| title | Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements |
| topic | Combinatorics Group Theory 52C35, 14N20, 32S22, 51D20 |
| url | https://arxiv.org/abs/2210.00436 |