Characteristic classes of complex hypersurfaces

Details Characteristic classes of complex hypersurfaces Characteristic classes of complex hypersurfaces

2009-08-22

arxiv.org/abs/0908.3240v3

Adv. Math. 225 (2010), no. 5, 2616-2647

Mathematics

Algebraic Topology

v2: title changed, exposition improved and expanded, references added

Scientific paper

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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