When are splitting loci Gorenstein?
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917050125910016 |
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| author | Lin, Feiyang |
| author_facet | Lin, Feiyang |
| contents | Splitting loci are certain natural closed substacks of the stack of vector bundles on $\mathbb{P}^1$, which have found interesting applications in the Brill-Noether theory of $k$-gonal curves. In this paper, we completely characterize when splitting loci, as algebraic stacks, are Gorenstein or $\mathbb{Q}$-Gorenstein. The main ingredients of the proof are a computation of the class groups of splitting loci in certain affine extension spaces, and a formula for the class of their canonical module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When are splitting loci Gorenstein? Lin, Feiyang Algebraic Geometry Commutative Algebra 14D20, 14M12, 14B05 Splitting loci are certain natural closed substacks of the stack of vector bundles on $\mathbb{P}^1$, which have found interesting applications in the Brill-Noether theory of $k$-gonal curves. In this paper, we completely characterize when splitting loci, as algebraic stacks, are Gorenstein or $\mathbb{Q}$-Gorenstein. The main ingredients of the proof are a computation of the class groups of splitting loci in certain affine extension spaces, and a formula for the class of their canonical module. |
| title | When are splitting loci Gorenstein? |
| topic | Algebraic Geometry Commutative Algebra 14D20, 14M12, 14B05 |
| url | https://arxiv.org/abs/2510.26044 |