2022/04/20 by Torsten Hoge, Gerhard Roehrle, Hoge, Torsten +1
Mathematics · #14N20 #32S22 #51D20 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2204.09540
openalex publication_date 2022/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (\mathcal A'',κ). 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'',κ). 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'',κ) -- irrespective of the freeness of \mathcal A. In addition, we show counterparts of the latter kind for additive and recursive freeness.