TY - JOUR
T1 - The Euler multiplicity and addition-deletion theorems for multiarrangements
AU - Abe, Takuro
AU - Terao, Hiroaki
AU - Wakefield, Max
N1 - Funding Information:
The first author is supported by the 21st Century COE Program ‘Mathematics of Nonlinear Structures via Singularities’, Hokkaido University. The second author is supported in part by the Japan Society for the Promotion of Science. The third author is supported by NSF grant # 0600893 and the NSF Japan program.
PY - 2008/4
Y1 - 2008/4
N2 - The addition-deletion theorems for hyperplane arrangements, which were originally shown by Terao [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 A3, to construct free and non-free multiarrangements.
AB - The addition-deletion theorems for hyperplane arrangements, which were originally shown by Terao [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 A3, to construct free and non-free multiarrangements.
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U2 - 10.1112/jlms/jdm110
DO - 10.1112/jlms/jdm110
M3 - Article
AN - SCOPUS:44649178712
SN - 0024-6107
VL - 77
SP - 335
EP - 348
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 2
ER -