RINGS OF DIFFERENTIAL-OPERATORS ON TORIC VARIETIES

Let H be a finite dimensional toric variety over an algebraically closed field of characteristic zero, k. Let D(H) be the sheaf of differential operators on H. We show that the ring of global sections, GAMMA(H, D(H)) is a finitely generated Noetherian k-algebra and that its generators can be explicitly found. We prove a similar result for the sheaf of differential operators with coefficients in a line bundle.