Dept. Math, Hokkaido Univ. EPrints Server

The e-multiplicity and addition-deletion theorems for multiarrangements

Preprint Series # 823
Abe, Takuro and Terao, Hiroaki and Wakefield, Max The e-multiplicity and addition-deletion theorems for multiarrangements. (2006);

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Abstract

The addition-deletion theorems for hyperplane arrangements, which were originally shown in [T1], 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 e-multiplicity, of a restricted multiarrangement. We compute the e-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.

Item Type:Preprint
Subjects:00-xx GENERAL
ID Code:1662