Index formula for MacPherson cycles of affine algebraic varieties

Details Index formula for MacPherson cycles of affine algebraic varieties Index formula for MacPherson cycles of affine algebraic varieties

2006-03-14

arxiv.org/abs/math/0603338v2

Tohoku Math. J. 62 (2010), 29-44

Mathematics

Algebraic Geometry

17 pages, shorter version, same results

Scientific paper

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-Tibar-Verjovsky global counterpart of the Le-Teissier formula for the local Euler obstruction.

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