Refined Brill-Noether Theory for Complete Graphs
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916561442308096 |
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| author | Aono, Haruku Burkholder, Eric Craig, Owen Dikobe, Ketsile Jensen, David Norris, Ella |
| author_facet | Aono, Haruku Burkholder, Eric Craig, Owen Dikobe, Ketsile Jensen, David Norris, Ella |
| contents | The divisor theory of the complete graph $K_n$ is in many ways similar to that of a plane curve of degree $n$. We compute the splitting types of all divisors on the complete graph $K_n$. We see that the possible splitting types of divisors on $K_n$ exactly match the possible splitting types of line bundles on a smooth plane curve of degree $n$. This generalizes the earlier result of Cori and Le Borgne computing the ranks of all divisors on $K_n$, and the earlier work of Cools and Panizzut analyzing the possible ranks of divisors of fixed degree on $K_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refined Brill-Noether Theory for Complete Graphs Aono, Haruku Burkholder, Eric Craig, Owen Dikobe, Ketsile Jensen, David Norris, Ella Combinatorics 05C57, 14H51 The divisor theory of the complete graph $K_n$ is in many ways similar to that of a plane curve of degree $n$. We compute the splitting types of all divisors on the complete graph $K_n$. We see that the possible splitting types of divisors on $K_n$ exactly match the possible splitting types of line bundles on a smooth plane curve of degree $n$. This generalizes the earlier result of Cori and Le Borgne computing the ranks of all divisors on $K_n$, and the earlier work of Cools and Panizzut analyzing the possible ranks of divisors of fixed degree on $K_n$. |
| title | Refined Brill-Noether Theory for Complete Graphs |
| topic | Combinatorics 05C57, 14H51 |
| url | https://arxiv.org/abs/2501.06083 |