Abstract
Let X be an algebraic variety defined over an algebraically closed field. We study the fiber of the Riemann–Zariski space above a closed point x∈X. If x is regular, we prove that its homeomorphism type only depends on the dimension of X. If x is a singular point of a normal surface, we show that it only depends on the dual graph of a good resolution of (X,x) up to some precise equivalence. Both results also hold for the normalized non-Archimedean link of x in X.
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