The Stacks project

Definition 76.6.5. Let $S$ be a scheme. Let $i : Z \to X$ be an immersion of algebraic spaces over $S$. The normal cone $C_ ZX$ of $Z$ in $X$ is

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

see Morphisms of Spaces, Definition 67.20.8. The normal bundle of $Z$ in $X$ is the vector bundle

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

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View Definition 76.6.5 as pdf