Strict transform
= Strict transform
{title2=$\widetilde Y$}
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The strict transform of a subvariety $Y$ under a blowup $\sigma:\widetilde X\to X$ is the closure of $\sigma^{-1}(Y\setminus Z)$, where $Z$ is the center. Its total transform also contains the <exceptional divisor> with the multiplicity with which $Y$ passes through $Z$.
= Proper transform
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