Resolving the Singularities of Splitting Loci
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908430052098048 |
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| author | Lin, Feiyang |
| author_facet | Lin, Feiyang |
| contents | We construct modular resolutions of singularities for splitting loci, and use them to show that tame splitting loci have rational singularities. As a corollary of our results and Hurwitz-Brill-Noether theory, we prove that if $C$ is a general $k$-gonal curve, the components of $W^r_d(C)$ have rational singularities. We also recover the classical Gieseker-Petri theorem. Along the way, we prove a cohomology vanishing statement for certain tautological vector bundles on $\operatorname{Quot}^{r,d}_{\mathbb{P}^1}(\mathcal{O}^{\oplus N})$, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resolving the Singularities of Splitting Loci Lin, Feiyang Algebraic Geometry 14H51, 14D20, 14M12 We construct modular resolutions of singularities for splitting loci, and use them to show that tame splitting loci have rational singularities. As a corollary of our results and Hurwitz-Brill-Noether theory, we prove that if $C$ is a general $k$-gonal curve, the components of $W^r_d(C)$ have rational singularities. We also recover the classical Gieseker-Petri theorem. Along the way, we prove a cohomology vanishing statement for certain tautological vector bundles on $\operatorname{Quot}^{r,d}_{\mathbb{P}^1}(\mathcal{O}^{\oplus N})$, which may be of independent interest. |
| title | Resolving the Singularities of Splitting Loci |
| topic | Algebraic Geometry 14H51, 14D20, 14M12 |
| url | https://arxiv.org/abs/2507.01233 |