A morphism of intersection homology induced by an algebraic map

Weber, Andrzej

doi:10.1090/S0002-9939-99-05081-9

A morphism of intersection homology induced by an algebraic map
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Proc. Amer. Math. Soc. 127 (1999), 3513-3516 Request permission

Abstract:

Let $f:X \rightarrow Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^{*}:IH^{*}(Y)\rightarrow IH^{*}(X)$ 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 $f^{*}$. Our construction is an easy application of the Decomposition Theorem.

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