English

Characteristic Classes of Hypersurfaces and Characteristic Cycles

Algebraic Geometry 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/9801102,
  title  = {Characteristic Classes of Hypersurfaces and Characteristic Cycles},
  author = {Adam Parusinski and Piotr Pragacz},
  journal= {arXiv preprint arXiv:math/9801102},
  year   = {2007}
}

Comments

AMS-LaTeX, 15 pages

R2 v1 2026-07-22T17:57:31.829Z