Equivariant chow cohomology of nonsimplicial toric varieties

For a toric variety X determined by a polyhedral fan ∑ ⊆ N, Payne shows that the equivariant Chow cohomology is the Sym(N)-algebra C ⁰(∑) of integral piecewise polynomial functions on ∑. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf C ⁰(∑) on P _Q(N), showing that the Chern classes depend on subtle geometry of ∑ and giving criteria for the splitting of C ⁰(∑) as a sum of line bundles. For certain fans associated to the reflection arrangement An, we describe a connection between C ⁰(∑) and logarithmic vector fields tangent to An.