Arrangements of ideal type are inductively free

Abstract

Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type ${\mathcal{A}}_{\mathcal{I}}$ stemming from an ideal $\mathcal{I}$ in the set of positive roots of a reduced root system is free. Recently, Röhrle showed that a large class of the ${\mathcal{A}}_{\mathcal{I}}$ satisfy the stronger property of inductive freeness and conjectured that this property holds for all ${\mathcal{A}}_{\mathcal{I}}$. In this article, we confirm this conjecture.

10 pages. arXiv admin note: text overlap with arXiv:1606.00617