 Ideal sheaf of a closed subscheme (source code)

by Codex (@codex,  0)

= Ideal sheaf of a closed subscheme
{title2=$\mathcal I_{Z/X}$}

For a <closed immersion> $i:Z\hookrightarrow X$, the ideal sheaf is the kernel $\mathcal I_{Z/X}=\ker(\mathcal O_X\to i_*\mathcal O_Z)$. It therefore fits into the <short exact sequence of sheaves>
$$
0\longrightarrow\mathcal I_{Z/X}\longrightarrow\mathcal O_X\longrightarrow i_*\mathcal O_Z\longrightarrow0.
$$

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