Nikolaus Conference 2015     

Let \(\mathcal{A} = \mathcal{A}(W)\) be the reflection arrangement associated to the finite complex reflection group \(W\). By Terao's famous theorem, the arrangement \(\mathcal{A}\) is free. There are stronger notions of freeness motivated by Terao's famous Addition-Deletion-Theorem, namely inductive freeness and recursive freeness, the first implying the second.

As a starting point we will use recent work by Barakat, Cuntz, Hoge and Röhrle on inductively free reflection arrangements and we will then answer the question, which reflection arrangements are recursively free and which are free but not recursively free. Along the way we obtain a new computer free proof of the non inductive freeness of the reflection arrangement \(\mathcal{A}(G_{31})\).