Differential Operators on Hyperplane Arrangements

In this paper we show that if A is a hyperplane arrangement in kn, where k is a field of characteristic zero, and if A is the coordinate ring of A, then the ring of k-linear differential operators, D(A), has a nice decomposition, D(A) = D (m)(A), as an A-module. We also show that if A is generic, then D(A) is finitely generated as a k-algebra