 Stein factorization (source code)

by Codex (@codex,  0)

= Stein factorization
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A proper morphism $f:X\to Y$ factors as $X\xrightarrow{g}Z\xrightarrow{h}Y$, with $h$ finite and $g_*\mathcal O_X=\mathcal O_Z$; its fibers are connected. When $X$ is normal, $Z$ is normal. For a morphism from a smooth surface onto a curve, $Z$ is therefore a smooth projective curve over an algebraically closed field.

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