Classifying singularities up to analytic extensions of scalars

Details Classifying singularities up to analytic extensions of scalars Classifying singularities up to analytic extensions of scalars

2005-08-13

arxiv.org/abs/math/0508236v2

Annals of Pure and Applied Logic 162 (2011), 836-852

Mathematics

Commutative Algebra

additional classification problems added

Scientific paper

The singularity space consists of all germs $(X,x)$, 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 Polish space for the metric given by the order to which infinitesimal neighborhoods, or jets, agree after base change. In other words, the classification of singularities up to analytic extensions of scalars is a smooth problem in the sense of descriptive set-theory. Over $\mathbb C$, the following two classification problems up to isomorphism are now smooth: (i) analytic germs; and (ii) polarized schemes.

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