The Euler multiplicity and addition–deletion theorems for multiarrangements
Takuro Abe, Hiroaki Terao, Max Wakefield
Source abstract
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 A 3 , to construct free and non‐free multiarrangements.
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