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Bivariant Intersection Theory

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

Summary

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.

Keywords

Vector Bundle Chern Class Exceptional Divisor Cartier Divisor Ideal Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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