Publication details

A bound for crystallographic arrangements

authored by
Michael Cuntz
Abstract

A crystallographic arrangement is a set of linear hyperplanes satisfying a certain integrality property and decomposing the space into simplicial cones. Crystallographic arrangements were completely classified in a series of papers by Heckenberger and the author. However, this classification is based on two computer proofs checking millions of cases. In the present paper, we prove without using a computer that, up to equivalence, there are only finitely many irreducible crystallographic arrangements in each rank greater than two.

Organisation(s)
Institute of Algebra, Number Theory and Discrete Mathematics
Type
Article
Journal
Journal of algebra
Volume
574
Pages
50-69
No. of pages
20
ISSN
0021-8693
Publication date
15.05.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Algebra and Number Theory
Electronic version(s)
https://arxiv.org/abs/1903.00300 (Access: Open)
https://doi.org/10.1016/j.jalgebra.2021.01.028 (Access: Closed)