Mathematics – Complex Variables
Scientific paper
2006-12-23
J. London Math. Soc. (2) 77 (2008), 335-348
Mathematics
Complex Variables
Scientific paper
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 $A_{3}$ to construct free and non-free multiarrangements.
Abe Takuro
Terao Hiroaki
Wakefield Max
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