Abstract
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 language | English (US) |
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Pages (from-to) | 4041-4051 |
Number of pages | 11 |
Journal | Transactions of the American Mathematical Society |
Volume | 364 |
Issue number | 8 |
DOIs | |
State | Published - 2012 |
Externally published | Yes |
Keywords
- Chow ring
- Piecewise polynomial function
- Toric variety
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics