Equivariant Chow cohomology of nonsimplicial toric varieties
Algebraic Geometry
2014-07-14 v2
Abstract
For a toric variety X_P determined by a rational polyhedral fan P in a lattice N, Payne shows that the equivariant Chow cohomology of X_P is the Sym(N)--algebra C^0(P) of integral piecewise polynomial functions on P. We use the Cartan-Eilenberg spectral sequence to analyze the associated reflexive sheaf on Proj(N), showing that the Chern classes depend on subtle geometry of P and giving criteria for the splitting of the sheaf as a sum of line bundles. For certain fans associated to the reflection arrangement A_n, we describe a connection between C^0(P) and logarithmic vector fields tangent to A_n.
Keywords
Cite
@article{arxiv.1101.0352,
title = {Equivariant Chow cohomology of nonsimplicial toric varieties},
author = {Hal Schenck},
journal= {arXiv preprint arXiv:1101.0352},
year = {2014}
}
Comments
11 pages 3 figures v2 references added, typos fixed