Loosely speaking, GL-varieties are affine schemes whose coordinate rings are polynomial representations. Their closed points can be obtained as the inverse limits of Vec-varieties, functors from the category of finite dimensional vector spaces to reduced affine varieties.

In a previous talk, we saw that the inverse limit of the singular loci of a Vec-variety defines a closed Vec-subvariety of “singular points”. In a forthcoming paper with Andrew Snowden, we show that the GL-variety arising from these "singular points" is the locus of singular points, in the classical sense, of the initial GL-variety.

In this talk, I will present the necessary background and the aforementioned result.