= Normal bundle of a smooth plane conic
{title2=$N_{C/\mathbf P^3}\cong\mathcal O(2)\oplus\mathcal O(4)$}
Embed a <smooth plane conic> in $\mathbf P^3$ through a plane. The plane equation and conic equation form a <regular sequence> of degrees one and two, so its <normal sheaf> is $\mathcal O_C(1)\oplus\mathcal O_C(2)$. Under $C\cong\mathbf P^1$, hyperplane degree is two, hence this <normal bundle> is $\mathcal O_{\mathbf P^1}(2)\oplus\mathcal O_{\mathbf P^1}(4)$. The normal exact sequence splits as well because $H^1(\mathbf P^1,\mathcal O(2))=0$.
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