I have a question about properties of Henselian ring/schemes exploited in M. Artin's article "On Isolated Rational Singularities of Surfaces":

Here the relevant excerpt:

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In the excerpt we start with schemes $V, \bar{V}=Spec(A)$ where $A$ is a local, normal $2$-dimensional ring with algebraically closed residue field $k$.

Let futhermore $\pi:V \to \bar{V}$ be birational proper map with $V$ regular, i.e. a "resolution" of the singularity of $\bar{V}$.

Denote by $Z= \sum_i X_i$ the fundamental cycle; here the definition:

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$Z$ is noting but the unique smallest cycle satisfying property (ii)

In order to verify $V \times_{\bar{V}} Spec(A/m^n)= nZ$ the author firstly replaces $A$ by it's henselisation $A_h$.

(1) My first question: Why this replacement can here be done wlog?

And my second question is:

Above in the excerpt the author claims that since $A$ is henselian (after replacing $A$ by $A_h$) one always can find a divisor $D$ with following essential property on intersection numbers

$$(D \cdot X_i) = - (Z \cdot X_i)$$.

(2) My second question is simply why the henselian property allows to find such divisor $D$?


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