Advanced Studies in Pure Mathematics

Weighted Chern–Mather classes and Milnor classes of hypersurfaces

Paolo Aluffi

Full-text: Open access


We introduce a class extending the notion of Chern–Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz–MacPherson’s Chern class and the class of the virtual tangent bundle of a singular hypersurface of a nonsingular variety. Applications include constraints on the possible singularities of a hypersurface and on contacts of nonsingular hypersurfaces, and multiplicity computations.

Article information

Singularities – Sapporo 1998, J.-P. Brasselet and T. Suwa, eds. (Tokyo: Mathematical Society of Japan, 2000), 1-20

Received: 11 November 1998
Revised: 18 March 1999
First available in Project Euclid: 20 August 2018

Permanent link to this document euclid.aspm/1534789547

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic) 14H30: Coverings, fundamental group [See also 14E20, 14F35]


Aluffi, Paolo. Weighted Chern–Mather classes and Milnor classes of hypersurfaces. Singularities – Sapporo 1998, 1--20, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02910001.

Export citation