A geometric condition for a hyperplane arrangement to be free
type: Item
instance of: scholarly article
title: A geometric condition for a hyperplane arrangement to be free
zbMATH Open document ID: 0905.05017
author: Joseph P. S. Kung
published in: Advances in Mathematics
publication date: 1999-01-14T00:00:00Z
review text: This paper collects and studies examples of arrangements obained by deleting ``few'' hyperplanes from a supersolvable (or even modularly complemented) hyperplane arrangement. Such a subarrangement can be free (in the sense of Terao) only if its characteristic polynomial factors over \({\mathbf Z}\). However, there are also many examples of non-free arrangements for which the characteristic polynomial factors. An effective method for proving non-freeness is to embed into a supersolvable arrangement and then to compare exponents in view of ``Tugger's condition''; compare the ``supersolvable resolutions'' of \textit{G. M. Ziegler} [Matroid representations and free arrangements, Trans. Am. Math. Soc. 320, No. 2, 525-541 (1990; Zbl 0727.05019)].
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 52C35
zbMATH DE Number: 1211556
reviewed by: Günter M. Ziegler
MaRDI profile type: Publication
full work available at URL: aima.1998.1722
OpenAlex ID: W1981470062
cites work: Modular elements of higher-weight Dowling lattices
cites work: Möbius inversion in lattices
cites work: Q5619114
cites work: Q5685088
cites work: A class of geometric lattices based on finite groups
cites work: A Counterexample to Orlik's Conjecture
cites work: Q3775655
cites work: Planar configurations which determine few slopes
cites work: Basic derivations for subarrangements of Coxeter arrangements
cites work: A classification of modularly complemented geometric lattices
cites work: Q4717847
cites work: Q4003206
cites work: Q3819084
cites work: Q4748256
cites work: 2N noncollinear points determine at least 2N directions
cites work: Dowling group geometries and the critical problem
cites work: Matroid Representations and free Arrangements
DOI: 10.1006/AIMA.1998.1722
description: scientific article; zbMATH DE number 1211556