Differential forms with logarithmic poles and Chern-Schwartz-MacPherson classes of singular varieties

P. Aluffi

We express the Chern-Schwartz-MacPherson class of a possibly singular variety in terms of the total Chern class of a bundle of forms with logarithmic poles. As an application, we obtain a formula for the Chern-Schwartz-MacPherson class of a hypersurface of a nonsingular variety, in terms of the Chern-Mather class of a suitable sheaf.