Characteristic classes of complex hypersurfaces
Abstract
The Milnor-Hirzebruch class of a locally complete intersection X in an algebraic manifold M measures the difference between the (Poincare dual of the) Hirzebruch class of the virtual tangent bundle of X and, respectively, the Brasselet-Schuermann-Yokura (homology) Hirzebruch class of X. In this note, we calculate the Milnor-Hirzebruch class of a globally defined algebraic hypersurface X in terms of the corresponding Hirzebruch invariants of singular strata in a Whitney stratification of X. Our approach is based on Schuermann's specialization property for the motivic Hirzebruch class transformation of Brasselet-Schuermann-Yokura. The present results also yield calculations of Todd, Chern and L-type characteristic classes of hypersurfaces.
Cite
@article{arxiv.0908.3240,
title = {Characteristic classes of complex hypersurfaces},
author = {Sylvain E. Cappell and Laurentiu Maxim and Joerg Schuermann and Julius L. Shaneson},
journal= {arXiv preprint arXiv:0908.3240},
year = {2012}
}
Comments
v2: title changed, exposition improved and expanded, references added