The Stacks project

Definition 54.14.2. Let $Y$ be a $2$-dimensional Noetherian integral scheme. We say $Y$ has a resolution of singularities by normalized blowups if there exists a sequence

\[ Y_ n \to Y_{n - 1} \to \ldots \to Y_1 \to Y_0 \to Y \]


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

  2. $Y_0 \to Y$ is the normalization,

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

  4. $Y_ n$ is regular.

Comments (2)

Comment #5839 by on

In the centered sequence of morphisms, the should be .

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