The Stacks project

Definition 31.19.5. Let $i : Z \to X$ be an immersion of schemes. The normal cone $C_ ZX$ of $Z$ in $X$ is

\[ C_ ZX = \underline{\mathop{\mathrm{Spec}}}_ Z(\mathcal{C}_{Z/X, *}) \]

see Constructions, Definitions 27.7.1 and 27.7.2. The normal bundle of $Z$ in $X$ is the vector bundle

\[ N_ ZX = \underline{\mathop{\mathrm{Spec}}}_ Z(\text{Sym}(\mathcal{C}_{Z/X})) \]

see Constructions, Definitions 27.6.1 and 27.6.2.

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