Geodesic
Motivic Milnor classes
Journal of Singularities, Tome 1 (2010), pp. 39-59

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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.
DOI : 10.5427/jsing.2010.1c
Classification : 
@article{10_5427_jsing_2010_1c,
     author = {Shoji Yokura},
     title = {Motivic {Milnor} classes},
     journal = {Journal of Singularities},
     pages = {39--59},
     publisher = {mathdoc},
     volume = {1},
     year = {2010},
     doi = {10.5427/jsing.2010.1c},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2010.1c/}
}
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%J Journal of Singularities
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Shoji Yokura. Motivic Milnor classes. Journal of Singularities, Tome 1 (2010), pp. 39-59. doi: 10.5427/jsing.2010.1c

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