Equivariant Chow Cohomology of Nonsimplicial Toric Varieties
نویسنده
چکیده
Abstract. For a toric variety XΣ determined by a polyhedral fan Σ ⊆ N , Payne shows that the equivariant Chow cohomology is the Sym(N)–algebra C(Σ) of integral piecewise polynomial functions on Σ. We use the CartanEilenberg spectral sequence to analyze the associated reflexive sheaf C(Σ) on PQ(N), showing that the Chern classes depend on subtle geometry of Σ and giving criteria for the splitting of C(Σ) as a sum of line bundles. For certain fans associated to the reflection arrangement An, we describe a connection between C(Σ) and logarithmic vector fields tangent to An.
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