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arXiv · 0908.3240

Characteristic classes of complex hypersurfaces

Sylvain E. Cappell·Laurentiu Maxim·Joerg Schuermann·Julius L. Shaneson
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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.

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BibTeXRIS

Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann, Julius L. Shaneson. 2009-11-30. Characteristic classes of complex hypersurfaces. https://arxiv.org/abs/0908.3240

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