Definition 87.8.2. Let $S$ be a scheme. Let $Y$ be a $2$-dimensional Noetherian integral algebraic space over $S$. We say $Y$ has a *resolution of singularities by normalized blowups* if there exists a sequence

where

$Y_ i$ is proper over $Y$ for $i = 0, \ldots , n$,

$Y_0 \to Y$ is the normalization,

$Y_ i \to Y_{i - 1}$ is a normalized blowup for $i = 1, \ldots , n$, and

$Y_ n$ is regular.

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