The Euler multiplicity and addition-deletion theorems for multiarrangements
复变函数
2014-02-26 v3 代数几何
组合数学
摘要
The addition-deletion theorems for hyperplane arrangements, which were originally shown in [H. Terao, Arrangements of hyperplanes and their freeness I, II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 27 (1980), 293--320], provide useful ways to construct examples of free arrangements. In this article, we prove addition-deletion theorems for multiarrangements. A key to the generalization is the definition of a new multiplicity, called the Euler multiplicity, of a restricted multiarrangement. We compute the Euler multiplicities in many cases. Then we apply the addition-deletion theorems to various arrangements including supersolvable arrangements and the Coxeter arrangement of type to construct free and non-free multiarrangements.
引用
@article{arxiv.math/0612739,
title = {The Euler multiplicity and addition-deletion theorems for multiarrangements},
author = {Takuro Abe and Hiroaki Terao and Max Wakefield},
journal= {arXiv preprint arXiv:math/0612739},
year = {2014}
}