Advanced Studies in Pure Mathematics

From Chern classes to Milnor classes – A history of characteristic classes for singular varieties

Jean-Paul Brasselet

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Abstract

In this paper, we give a survey and recent developments about the definitions of characteristic classes for possibly singular complex analytic (or algebraic) varieties. We recall the classical construction of characteristic classes in the case of manifolds, by obstruction theory and using Schubert cycles. Then, we present various generalizations of characteristic classes to singular varieties, due to M.H. Schwartz, W.T. Wu, J. Mather, R. MacPherson, W. Fulton and K. Johnson and we discuss relations among these definitions. More recent results concern the definition and properties of so-called Milnor classes, as developped by P. Aluffi, J.P. Brasselet-D. Lehmann-J. Seade-T. Suwa, A. Parusiński-P. Pragacz and S. Yokura.

Article information

Source
Singularities – Sapporo 1998, J.-P. Brasselet and T. Suwa, eds. (Tokyo: Mathematical Society of Japan, 2000), 31-52

Dates
Received: 9 August 1999
Revised: 7 February 2000
First available in Project Euclid: 20 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534789549

Digital Object Identifier
doi:10.2969/aspm/02910031

Mathematical Reviews number (MathSciNet)
MR1819629

Zentralblatt MATH identifier
1036.32022

Citation

Brasselet, Jean-Paul. From Chern classes to Milnor classes – A history of characteristic classes for singular varieties. Singularities – Sapporo 1998, 31--52, Mathematical Society of Japan, Tokyo, Japan, 2000. doi:10.2969/aspm/02910031. https://projecteuclid.org/euclid.aspm/1534789549


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