Equivariant chow cohomology of nonsimplicial toric varieties

Hal Schenck

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)4041-4051
Number of pages11
JournalTransactions of the American Mathematical Society
Issue number8
StatePublished - 2012
Externally publishedYes


  • Chow ring
  • Piecewise polynomial function
  • Toric variety

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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