Characteristic Classes of Hypersurfaces and Characteristic Cycles

Details Characteristic Classes of Hypersurfaces and Characteristic Cycles Characteristic Classes of Hypersurfaces and Characteristic Cycles

1998-01-21

arxiv.org/abs/math/9801102v1

Mathematics

Algebraic Geometry

AMS-LaTeX, 15 pages

Scientific paper

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface. Two different approaches are presented. The first is based on the theory of characteristic cycle and the works of Sabbah, Briancon-Maisonobe-Merle, and Le-Mebkhout. In particular, this approach leads to a simple proof of a formula of Aluffi for the above mentioned class. The second approach uses Verdier's specialization property of the Chern-Schwartz-MacPherson classes. Some related new formulas are also given.

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