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The word normalization refers to a procedure transforming an algebraic variety (more generally, a scheme) to a normal one via a birational morphism. This tag should be used only for questions in algebraic geometry rather than ones in analysis, logic or probability.

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Is weak normality stable under completion?

Here is a partial solution: modulo a problem of constructing "sufficiently generic" elements in the maximal ideal of a reduced noetherian local ring of dimension > 1 (in a sense made precise at the en …