Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Singularities – Sapporo 1998, J.-P. Brasselet and T. Suwa, eds. (Tokyo: Mathematical Society of Japan, 2000), 31 - 52
From Chern classes to Milnor classes – A history of characteristic classes for singular varieties
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.
Received: 9 August 1999
Revised: 7 February 2000
First available in Project Euclid: 20 August 2018
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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