D-Modules on smooth toric varieties

Let X be a smooth toric variety. Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal b. Let A denote the ring of differenti al operators on Spec(S). We show that the category of D-modules on X is equ ivalent to a subcategory of graded A-modules module b-torsion. Additionally , we prove that the characteristic variety of a D-module is a geometric quo tient of an open subset of the characteristic variety of the associated A-m odule and that holonomic D-modules correspond to holonomic A-modules. (C) 2 001 Academic Press.