Classes de Chern des varietes singulieres, revisitees

Details Classes de Chern des varietes singulieres, revisitees Classes de Chern des varietes singulieres, revisitees

2006-01-18

arxiv.org/abs/math/0601453v1

C. R. Math. Acad. Sci. Paris 342 (2006), no. 6, 405-410

Mathematics

Algebraic Geometry

6 pages; to appear in the CRAS

Scientific paper

10.1016/j.crma.2006.01.002

We introduce a notion of `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: Kwiecinski's product formula, and the Ehlers-Barthel-Brasselet-Fieseler computation of Chern-Schwartz-MacPherson classes of toric varieties.

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