On a Verdier-type Riemann–Roch for Chern–Schwartz–MacPherson class

Abstract

We show that a Verdier-type Riemann–Roch formula holds for the Chern–Schwartz–MacPherson transformation C ∗: F→A ∗ in the case of smooth morphisms, but that it does not hold for local complete intersection morphisms in general. And we show that for Euler local complete intersection morphisms there is a reasonable problem and that its very special case turns out to be nothing but the problem of comparing Chern–Schwartz–MacPherson class and Fulton's canonical class, which seems to require a generalization of the Milnor number.