Deformation to the Normal Cone

William Fulton ()
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William Fulton: University of Michigan, Department of Mathematics

Chapter Chapter 5 in Intersection Theory, 1998, pp 86-91 from Springer

Abstract: 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.

Keywords: Vector Bundle; Normal Cone; Normal Bundle; Exceptional Divisor; Graph Construction (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-1700-8_6

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