Correspondence Homomorphisms for Singular Varieties, by Eric M. Friedlander and Barry Mazur

An effective Chow correspondence $f: X \to C_{r,d}(Y)$ of relative dimension $r$ relating complex projective varieties $X, Y$ determines a cycle in the product $X\times Y$. The authors investigate the induced Chow correspondence homomorphism $f_*: H_*(X) \to H_{*+2r}(Y)$. This extends to singular varieties $X$ a familiar construction in classical algebraic geometry. The authors suggest that $f_*$ can be considered as a characteristic class for the family of cycles over $X$ associated to $f$. The constructions presented in this paper enable the authors to extend to singular varieties their earlier results on filtations in homology associated to Lawson homology; indeed, earlier results are further strengtened in that conclusions are obtained for integer (rather than rational) coefficients.

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