Mumford rigidity lemma (source code)

= Mumford rigidity lemma
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{wiki=Rigidity_lemma}

One form of Mumford's rigidity lemma says that if $X$ is complete, $Y$ is connected, and a morphism $f:X\times Y\to Z$ maps one fiber $X\times\{y_0\}$ to a point, then $f$ factors through the projection to $Y$ under the usual pointed hypotheses.