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Deformation to the Normal Cone

In: Intersection Theory

Author

Listed:
  • William Fulton

    (University of Michigan, Department of Mathematics)

Abstract

If X is a closed subscheme of Y, there is a family of imbeddings X S Y , parametrized by S 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.

Suggested Citation

  • William Fulton, 1998. "Deformation to the Normal Cone," Springer Books, in: Intersection Theory, edition 0, chapter 0, pages 86-91, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1700-8_6
    DOI: 10.1007/978-1-4612-1700-8_6
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