The singular locus of a GL-variety
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913172086063104 |
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| author | Chiu, Christopher Heng Danelon, Alessandro Snowden, Andrew |
| author_facet | Chiu, Christopher Heng Danelon, Alessandro Snowden, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30726 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The singular locus of a GL-variety Chiu, Christopher Heng Danelon, Alessandro Snowden, Andrew Algebraic Geometry 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. |
| title | The singular locus of a GL-variety |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.30726 |