Torus embeddings and algebraic intersection complexes

In [GM2], Goreskey and MacPherson defined and constructed intersection complexes for topological pseudomanifolds. The complexes are defined in the derived category of sheaves of modules over a constant ring sheaf. Since analytic spaces are of this category, any algebraic variety defined over C has an intersection complex for each perversity. The purpose of this paper is to give an algebraic description of the intersection complex of a toric variety. Namely, we describe it as a finite complex of coherent sheaves whose coboudary map is a differential operator of order one. Let Zh be the complete toric variety associated to a complete fan ∆. For each σ ∈ ∆, let X(σ)h be the associated closed subvariety of Zh. For each perversity p, ∗Supported in part by a Grant under The Monbusho International Scientific Research Program: 04044081