A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes

By Joerg Schuermann. 2002

52 citations recorded by the source corpus.

We give a general formula for the defect appearing in the Verdier-type Riemann-Roch formula for Chern-Schwartz-MacPherson classes in the case of a regular embedding. Our proof of this formula uses the constructible function version of Verdier's specialization functor, together with a specialization property of Chern-Schwartz-MacPherson classes and the corresponding Riemann-Roch theorem for smooth morphisms. As a very special case we get a formula for the Milnor-class of a local complete intersection in a smooth manifold, which in the case of a hypersurface gives back a result of Parusinski-Pragacz.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4b9d80da3688e980c9defc1b30d696ce401e39b5

Citations in the corpus

• Equivariant Chern classes of singular algebraic varieties with group actions (2004, unknown): “1 [25]), which describes the defect C∗◦f −f ◦C∗ in terms of the generalized vanishing cycle functor.”