The emultiplicity and additiondeletion theorems for multiarrangements
Preprint Series # 823 Abe, Takuro and Terao, Hiroaki and Wakefield, Max The emultiplicity and additiondeletion theorems for multiarrangements. (2006); AbstractThe additiondeletion theorems for hyperplane arrangements, which
were originally shown in [T1], provide useful ways to construct examples
of free arrangements. In this article, we prove additiondeletion theorems
for multiarrangements. A key to the generalization is the definition of
a new multiplicity, called the emultiplicity, of a restricted multiarrangement.
We compute the emultiplicities in many cases. Then we apply the
additiondeletion theorems to various arrangements including supersolvable
arrangements and the Coxeter arrangement of type A3 to construct
free and nonfree multiarrangements.
