Reflection arrangements are hereditarily free
Group Theory
2012-11-06 v2 Commutative Algebra
Abstract
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let A = A(W) be the associated hyperplane arrangement of W. Terao has shown that each such reflection arrangement A is free. Let L(A) be the intersection lattice of A. For a subspace X in L(A) we have the restricted arrangement A^X in X by means of restricting hyperplanes from A to X. In 1992, Orlik and Terao conjectured that each such restriction is again free. In this note we settle the outstanding cases confirming the conjecture.
Keywords
Cite
@article{arxiv.1205.5430,
title = {Reflection arrangements are hereditarily free},
author = {Torsten Hoge and Gerhard Roehrle},
journal= {arXiv preprint arXiv:1205.5430},
year = {2012}
}
Comments
6 pages; to appear in Tohoku Math. J