Recursively free reflection arrangements

Abstract

Let $\mathcal{A}=\mathcal{A}(W)$ be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement $\mathcal{A}$ is free. In this paper we classify all reflection arrangements which belong to the smaller class of recursively free arrangements. Moreover for the case that $W$ admits an irreducible factor isomorphic to $G_{31}$ we obtain a new (computer free) proof for the non-inductive freeness of $\mathcal{A}(W)$. Since our classification implies the non-recursive freeness of the reflection arrangement $\mathcal{A}(G_{31})$, we can prove a conjecture by Abe about the new class of divisionally free arrangements which he recently introduced.

26 pages, 3 figures. Corrected typos, added reference in section 5. Results unchanged

References in corpus (4)

• Free filtrations of affine Weyl arrangements and the ideal-Shi arrangements
• Non-recursive freeness and non-rigidity of plane arrangements
• Divisionally free Restrictions of Reflection Arrangements
• Inductive and Recursive Freeness of Localizations of Multiarrangements

Cited by in corpus (2)

• On the generation of rank 3 simple matroids with an application to Terao's freeness conjecture
• MAT-free reflection arrangements