Deformation to the Normal Cone

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

Summary

If X is a closed subscheme of Y, there is a family of imbeddings XY t , parametrized by t ∈ ℙ1, such that for t = 0 (in fact for t ≠ ∞) the imbedding is the given imbedding of X in Y, and for t = ∞ one has the zero section imbedding of X in the normal cone C X Y. The existence of such a deformation, together with the “principle of continuity” that intersection products should vary nicely in families, explains the prominent role to be played by the normal cone in constructing intersection products.

Keywords

Bedding 

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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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