Classes de Chern des variétés singulières, revisitées

Abstract

We introduce the notion of a proChow group of varieties, agreeing with the notion of Chow group for complete varieties and covariantly functorial with respect to 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. To cite this article: P. Aluffi, C. R. Acad. Sci. Paris, Ser. I 342 (2006).