Chern classes for singular hypersurfaces

Aluffi, Paolo

doi:10.1090/S0002-9947-99-02256-4

Chern classes for singular hypersurfaces
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by Paolo Aluffi

Trans. Amer. Math. Soc. 351 (1999), 3989-4026

DOI: https://doi.org/10.1090/S0002-9947-99-02256-4

Published electronically: February 8, 1999

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Abstract:

We prove a formula expressing the Chern-Schwartz-MacPherson class of a hypersurface in a nonsingular variety as a variation on another definition of the homology Chern class of singular varieties, introduced by W. Fulton; and we discuss the relation between these classes and others, such as Mather’s Chern class and the $\mu$-class we introduced in previous work.

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