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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24997 |
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| _version_ | 1866908914454364160 |
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| author | Bongiorno, Federico |
| author_facet | Bongiorno, Federico |
| contents | Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical singularities, its stabiliser group is a finite extension of an algebraic torus, thus, étale locally, the good moduli space exists. If the singularity is canonical, we further show that the locus of stable points is non-empty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularities of Foliations and Good Moduli Spaces of Algebraic Stacks Bongiorno, Federico Algebraic Geometry Representation Theory 14D23 (Primary) 14E15, 14B20 (Secondary) Drawing on the theory of Minimal Model Program singularities for foliations, we define relative canonical and log-canonical singularities for algebraic stacks with finite generic stabilisers. We show that if a point has log-canonical singularities, its stabiliser group is a finite extension of an algebraic torus, thus, étale locally, the good moduli space exists. If the singularity is canonical, we further show that the locus of stable points is non-empty. |
| title | Singularities of Foliations and Good Moduli Spaces of Algebraic Stacks |
| topic | Algebraic Geometry Representation Theory 14D23 (Primary) 14E15, 14B20 (Secondary) |
| url | https://arxiv.org/abs/2603.24997 |