“…If cl * = c * is the Chern class transformation, the problem amounts to comparing the Fulton-Johnson class c F J * (X) := c vir * (X) (e.g., see [16,17]) with the homology Chern class c * (X) of MacPherson. The difference between these two classes is measured by the so-called Milnor class M * (X) of X, which is studied in many references like [1,6,7,8,27,29,34,35,45]. This is a homology class supported on the singular locus of X, and for a global hypersurface it was computed in [29] (see also [34,35,45,27]) as a weighted sum in the Chern-MacPherson classes of closures of singular strata of X, the weights depending only on the normal information to the strata.…”