Correspondences

  • William Fulton
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 2)

Summary

A correspondence from X to Y, denoted α: XY, is a subvariety, cycle, or equivalence class of cycles on X × Y. The graph of a morphism, or the closure of the graph of a rational map, are basic examples, but more general correspondences have played an important role in the development of algebraic geometry. On complete non-singular varieties correspondences have a product β ∘ α, and a correspondence α: XY determines homomorphisms α* from A(X) to A(Y), and α* from A(Y) to A(X), these notions generalizing composition, push-forward, and pull-back for morphisms. The basic algebra of correspondences is deduced easily from the general theory of Chap. 8.

Keywords

Manifold Tate 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • William Fulton
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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