A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes
Algebraic Geometry
2007-05-23 v1 Complex Variables
Abstract
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.
Cite
@article{arxiv.math/0202175,
title = {A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes},
author = {Joerg Schuermann},
journal= {arXiv preprint arXiv:math/0202175},
year = {2007}
}
Comments
23 pages, no figures