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.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).