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arXiv · 2605.30726

The singular locus of a GL-variety

Christopher Heng Chiu·Alessandro Danelon·Andrew Snowden
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Abstract

A $\mathbf{GL}$-variety is a (typically) infinite dimensional variety $X$ equipped with an action of the infinite general linear group. In recent work of the first two authors with Draisma, a candidate definition for the singular locus of $X$ was put forth. The approach there made use of auxiliary finite dimensional varieties associated to $X$. In this paper, we give a number of characterizations of the singular locus that are intrinsic to $X$. This work shows that the candidate definition is clearly correct, and helps clarify the geometric meaning of singular points.

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Christopher Heng Chiu, Alessandro Danelon, Andrew Snowden. 2026-05-29. The singular locus of a GL-variety. https://arxiv.org/abs/2605.30726

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