Lemma 70.18.3. In the situation of Definition 70.18.1.

The strict transform $X'$ of $X$ is the blowup of $X$ in the closed subspace $f^{-1}Z$ of $X$.

For a quasi-coherent $\mathcal{O}_ X$-module $\mathcal{F}$ the strict transform $\mathcal{F}'$ is canonically isomorphic to the pushforward along $X' \to X \times _ B B'$ of the strict transform of $\mathcal{F}$ relative to the blowing up $X' \to X$.

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