Journal of Singularities
volume 1 (2010), 39-59
Received 10 September 2009. Received in revised form 5 January 2010.
The Milnor class is a generalization of the Milnor number, defined as the difference (up to sign) of Chern--Schwartz--MacPherson's class and Fulton--Johnson's canonical Chern class of a local complete intersection variety in a smooth variety. In this paper we introduce a "motivic" Grothendieck group and natural transformations from this Grothendieck group to the homology theory. We capture the Milnor class, more generally Milnor--Hirzebruch class, as a special value of a distinguished element under these natural transformations. We also show a Verdier-type Riemann--Roch formula for our motivic Milnor--Hirzebruch class. We use Fulton--MacPherson's bivariant theory and the motivic Hirzebruch class.
Mathematical Subject Classification:
Department of Mathematics and Computer Science
Faculty of Science
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