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Normalization is a fundamental ring-theoretic operation; geometrically itresolves singularities in codimension one. Existing algorithmic methods forcomputing the normalization rely on a common recipe: successively enlarge thegiven ring in form an endomorphism ring of a certain (fractional) ideal untilthe process becomes stationary. While Vasconcelos' method uses the dualJacobian ideal, Grauert-Remmert-type algorithms rely on so-called test ideals.  For algebraic varieties, one can apply such normalization algorithmsglobally, locally, or formal analytically at all points of the variety. In thispaper, we relate the number of iterations for global Grauert-Remmert-typenormalization algorithms to that of its local descendants.  We complement our results by an explicit study of ADE singularities. Thisincludes the description of the normalization process in terms of valuesemigroups of curves. It turns out that the intermediate steps produce only ADEsingularities and simple space curve singularities from the list ofFruehbis-Krueger.

Local analysis of Grauert-Remmert-type normalization algorithms