Classifying singularities up to analytic extensions of scalars is smooth

Annals of Pure and Applied Logic 162 (10):836-852 (2011)
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The singularity space consists of all germs , with X a Noetherian scheme and x a point, where we identify two such germs if they become the same after an analytic extension of scalars. This is a complete, separable space for the metric given by the order to which jets agree after base change. In the terminology of descriptive set-theory, the classification of singularities up to analytic extensions of scalars is a smooth problem. Over , the following two classification problems up to isomorphism are then also smooth: analytic germs; and polarized schemes



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