Classes de Chern pour variétés singulières, revisitées

Paolo Aluffi

We introduce the notion of {\em proChow group\/} of varieties, agreeing with the notion of Chow group for complete varieties and covariantly functorial with respect to {\em arbitrary\/} morphisms. We construct a natural transformation from the functor of constructible functions to the proChow functor, extending MacPherson's natural transformation. We illustrate the result by providing very short proofs of (a generalization of) two well-known facts on Chern-Schwartz-MacPherson classes.