Chern classes for singular hypersurfaces

Abstract

We prove a formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology Chern class of singular varieties, introduced by W. Fulton; and we discuss the relation between these classes and others, such as Mather’s Chern class and the μ \mu -class we introduced in previous work.