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.
- Chow ring
- Piecewise polynomial function
- Toric variety
ASJC Scopus subject areas
- Applied Mathematics