Some characterizations of freeness of hyperplane arrangement
Combinatorics
2007-05-23 v2 Algebraic Geometry
Abstract
We will consider some characterizations of freeness of a hyperplane arrangement, in terms of the following properties: locally freeness, factorization of characteristic polynomial and freeness of restricted multiarrangement. In the case of 3-arrangement, freeness is characterized by factorization of characteristic polynomial and coincidence of its roots with exponents of restricted multiarrangement. In the case of higher dimension, it is characterized by a kind of locally freeness and freeness of restricted multiarrangement. As an application, we prove the freeness of certain arrangements which is conjectured by Edelman and Reiner.
Keywords
Cite
@article{arxiv.math/0306228,
title = {Some characterizations of freeness of hyperplane arrangement},
author = {Masahiko Yoshinaga},
journal= {arXiv preprint arXiv:math/0306228},
year = {2007}
}