  We introduce a class extending the notion of Chern-Mather class to possibly
nonreduced schemes, and use it to express the difference between
Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle
of a singular hypersurface of a nonsingular variety. Applications include
constraints on the possible singularities of a hypersurface and on contacts of
nonsingular hypersurfaces, and multiplicity computations.
