The Stacks project

Lemma 31.14.2. Let $S$ be a scheme and let $D \subset S$ be an effective Cartier divisor. Then the conormal sheaf is $\mathcal{C}_{D/S} = \mathcal{I}_ D|_ D = \mathcal{O}_ S(-D)|_ D$ and the normal sheaf is $\mathcal{N}_{D/S} = \mathcal{O}_ S(D)|_ D$.

Proof. This follows from Morphisms, Lemma 29.31.2. $\square$

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