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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2604.26193 |
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| _version_ | 1866917445204180992 |
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| author | Aggarwal, Daksh |
| author_facet | Aggarwal, Daksh |
| contents | Given a curve $C$ that is a degree $k$ cover $C \to \mathbb{P}^1$ totally ramified at two points $p$ and $q$, we can seek to understand the space of degree $d$ line bundles on $C$ with prescribed ramification at $p$ and $q$. The corresponding subschemes of $\text{Pic}^d(C)$ are called transmission loci and are parameterized via elements of the (extended) $k$-affine symmetric group $\widetildeΣ_k$. Transmission loci provide a refinement of the splitting loci that have recently been extensively studied for $k$-gonal curves. Pflueger has conjectured analogues of the classic Brill-Noether theorem should hold for transmission loci. In this paper we prove Pflueger's conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Brill-Noether theory for totally ramified covers of the projective line Aggarwal, Daksh Algebraic Geometry 14H51 Given a curve $C$ that is a degree $k$ cover $C \to \mathbb{P}^1$ totally ramified at two points $p$ and $q$, we can seek to understand the space of degree $d$ line bundles on $C$ with prescribed ramification at $p$ and $q$. The corresponding subschemes of $\text{Pic}^d(C)$ are called transmission loci and are parameterized via elements of the (extended) $k$-affine symmetric group $\widetildeΣ_k$. Transmission loci provide a refinement of the splitting loci that have recently been extensively studied for $k$-gonal curves. Pflueger has conjectured analogues of the classic Brill-Noether theorem should hold for transmission loci. In this paper we prove Pflueger's conjectures. |
| title | Brill-Noether theory for totally ramified covers of the projective line |
| topic | Algebraic Geometry 14H51 |
| url | https://arxiv.org/abs/2604.26193 |