Advanced Studies in Pure Mathematics

Weighted Chern–Mather classes and Milnor classes of hypersurfaces

Paolo Aluffi

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534789547

Digital Object Identifier
doi:10.2969/aspm/02910001

Mathematical Reviews number (MathSciNet)
MR1819626

Zentralblatt MATH identifier
1077.14506

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

Citation

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. https://projecteuclid.org/euclid.aspm/1534789547


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