A morphism of intersection homology induced by an algebraic map

Abstract

Let $f:X-->Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^{\ast }:I{H}^{\ast }(Y)-->I{H}^{\ast }(X)$ compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism $f^{\ast }$. Our construction is an easy application of the Decomposition Theorem.

3 pages, AMS-TeX