Tohoku Math. J. (2) 62 (1), 29-44, (2010) DOI: 10.2748/tmj/1270041025
Jörg Schürmann, Mihai Tibăr
KEYWORDS: characteristic classes, constructible function, affine polar varieties, Euler obstruction, index theorem, characteristic cycles, stratified Morse theory, 14C25, 14C17, 14R25, 32S60, 14D06, 32S20
We give explicit MacPherson cycles for the Chern-MacPherson class of a closed affine algebraic variety $X$ and for any constructible function $\alpha$ with respect to a complex algebraic Whitney stratification of $X$.
We define generalized degrees of the global polar varieties and of the MacPherson cycles and we prove a global index formula for the Euler characteristic of $\alpha$. Whenever $\alpha$ is the Euler obstruction of $X$, this index formula specializes to the Seade-Tibăr-Verjovsky global counterpart of the Lê-Teissier formula for the local Euler obstruction.