Classifying singularities up to analytic extensions of scalars
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
