Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- 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
Characteristic classes of singular varieties
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.
Received: 8 June 2004
Revised: 28 February 2005
First available in Project Euclid: 3 January 2019
Permanent link to this document
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
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. https://projecteuclid.org/euclid.aspm/1546543243