## Advanced Studies in Pure Mathematics

### Characteristic classes of singular varieties

Adam Parusiński

#### Abstract

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

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1546543243

Digital Object Identifier
doi:10.2969/aspm/04310347

Mathematical Reviews number (MathSciNet)
MR2325145

Zentralblatt MATH identifier
1127.14009

#### Citation

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