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arXiv · 2204.09540

Inductive Freeness of Ziegler's Canonical Multiderivations

Torsten Hoge·Gerhard Roehrle
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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 $(\mathcal A'',\kappa)$. The aim of this paper is to prove an analogue of Ziegler's theorem for the stronger notion of inductive freeness: if $\mathcal A$ is inductively free, then so is the multiarrangement $(\mathcal A'',\kappa)$. In a related result we derive that if a deletion $\mathcal A'$ of $\mathcal A$ is free and the corresponding restriction $\mathcal A''$ is inductively free, then so is $(\mathcal A'',\kappa)$ -- irrespective of the freeness of $\mathcal A$. In addition, we show counterparts of the latter kind for additive and recursive freeness.

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BibTeXRIS

Torsten Hoge, Gerhard Roehrle. 2022-04-20. Inductive Freeness of Ziegler's Canonical Multiderivations. https://arxiv.org/abs/2204.09540

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