Institution: | a Department of Mathematics, Royal Institute of Technology, S-10044, Stockholm, Sweden b Department of Mathematics, Faculty of Science, University of Kagoshima, Kagoshima 890, Japan c Department of Mathematics, College of Liberal Arts, University of Kagoshima, Kagoshima 890, Japan |
Abstract: | We construct a functor, which we call the topological Radon transform, from a category of complex algebraic varieties with morphisms given by divergent diagrams, to constructible functions. The topological Radon transform is thus the composition of a pull-back and a push-forward of constructible functions. We show that the Chern-Schwartz-MacPherson transformation makes the topological Radon transform of constructible functions compatible with a certain homological Verdier-Radon transform. We use this set-up to prove, given a projective variety X, a formula for the Chern-Mather class of the dual variety in terms of that of X. |