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Tohoku Mathematical Journal
SECOND SERIES VOL. 62, NO. 1
|Tohoku Math. J.|
62 (2010), 29-44
INDEX FORMULA FOR MACPHERSON CYCLES OF AFFINE ALGEBRAIC VARIETIES
Jörg Schürmann and Mihai Tibăr
(Received October 17, 2008, revised July 28, 2009)
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.
2000 Mathematics Subject Classification.
Primary 14C25; Secondary 14C17, 14R25, 32S60, 14D06, 32S20.
Key words and phrases.
Characteristic classes, constructible function, affine polar varieties, Euler obstruction, index theorem, characteristic cycles, stratified Morse theory.
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