Advanced Studies in Pure Mathematics

Characteristic classes of singular varieties

Adam Parusiński

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This is a short and concise survey on recent results on the Milnor classes of global complete intersections. By definition the Milnor class of $X$ equals the difference between the Chern-Schwartz-MacPherson and the Fulton-Johnson classes of $X$ and we describe the results that express it in terms of the local and global invariants of the singular locus of $X$. In this survey we underline the characteristic cycle approach and its realtion to the vanishing Euler characteristic, as for instance to the Euler characteristic of the Milnor fibre in the hypersurface case.

Article information

Singularity Theory and Its Applications, S. Izumiya, G. Ishikawa, H. Tokunaga, I. Shimada and T. Sano, eds. (Tokyo: Mathematical Society of Japan, 2006), 347-367

Received: 8 June 2004
Revised: 28 February 2005
First available in Project Euclid: 3 January 2019

Permanent link to this document euclid.aspm/1546543243

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14J70: Hypersurfaces 32S25: Surface and hypersurface singularities [See also 14J17] 14P25: Topology of real algebraic varieties

Chern-Schwartz-MacPherson class Fulton-Johnson class characteristic cycle Milnor fibre vanishing Euler characteristic Stiefel-Whitney class


Parusiński, Adam. Characteristic classes of singular varieties. Singularity Theory and Its Applications, 347--367, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04310347.

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