Coxeter and crystallographic arrangements are inductively free

Abstract

Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of type $E_8$. With little extra work we prove that also all Coxeter arrangements are inductively free.

22 pages

References in corpus (2)

• An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization
• Crystallographic arrangements: Weyl groupoids and simplicial arrangements

Cited by in corpus (9)

• Rationally smooth Schubert varieties and inversion hyperplane arrangements
• Computing the nonfree locus of the moduli space of arrangements and Terao's freeness conjecture
• MAT-free reflection arrangements
• Recursively free reflection arrangements
• Strongly symmetric smooth toric varieties
• Arrangements of ideal type
• Combinatorics of free and simplicial line arrangements
• Combinatorial data of a free arrangement and the Terao conjecture
• Combinatorial simpliciality of arrangements of hyperplanes