2 00 8 Piecewise Polynomials , Minkowski Weights , and Localization on Toric Varieties

We use localization to describe the restriction map from equi-variant Chow cohomology to ordinary Chow cohomology for complete toric varieties in terms of piecewise polynomial functions and Minkowski weights. We compute examples showing that this map is not surjective in general, and that its kernel is not always generated in degree one. We prove a localization formula for mixed volumes of lattice polytopes and, more generally, a Bott residue formula for toric vector bundles.