Lemma 54.12.3. Let $(A, \mathfrak m, \kappa )$ be a local normal Nagata domain of dimension $2$ which defines a rational singularity, whose completion is normal, and which is Gorenstein. Then there exists a finite sequence of blowups in singular closed points

such that $X_ n$ is regular and such that each intervening schemes $X_ i$ is normal with finitely many singular points of the same type.

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