Bivariant Intersection Theory

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


Our basic intersection construction has assigned to a regular imbedding (or l.c.i. morphism) f: XY of codimension d a collection of homomorphisms
$$f^!:A_k Y' \to A_{k - d} X'$$
for all Y′ → Y, X′ = X × Y Y′, all k. In this chapter we formalize the study of such operations. For any morphism f: XY, a bivariant class c in \(A^p \left( {X\mathop \to \limits^f Y} \right)\) is a collection of homomorphisms from A k Y′ to A k−p X′, for all Y′ → Y, all k, compatible with push-forward, pull-back, and intersection products.


Vector Bundle Chern Class Exceptional Divisor Cartier Divisor Ideal Sheaf 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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