Deformation to the Normal Cone
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If X is a closed subscheme of Y, there is a family of imbeddings X ↪ Y 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.
KeywordsVector Bundle Normal Cone Normal Bundle Exceptional Divisor Graph Construction
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