Situation 54.9.1. Here $(A, \mathfrak m, \kappa )$ be a local normal Nagata domain of dimension $2$ which defines a rational singularity. Let $s$ be the closed point of $S = \mathop{\mathrm{Spec}}(A)$ and $U = S \setminus \{ s\} $. Let $f : X \to S$ be a modification with $X$ normal. We denote $C_1, \ldots , C_ r$ the irreducible components of the special fibre $X_ s$ of $f$.
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