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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.13208 |
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| _version_ | 1866909963017781248 |
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| author | Capobianco, Giusi Zheng, Angelina |
| author_facet | Capobianco, Giusi Zheng, Angelina |
| contents | We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill--Noether rank of a tropical curve. We recall Coppens' counterexample of Martens-special chain of cycles, and we generalize the construction defining another class of graphs, Martens-special trees of cycles, for which the conjecture does not hold in a similar setting. These are not the only counterexamples. However, we prove that the conjecture holds for all metric graphs with a stricter assumption on the degree in the Brill--Noether rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13208 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A tropical version of Martens' theorem for metric graphs Capobianco, Giusi Zheng, Angelina Combinatorics Algebraic Geometry 05C25, 14T15 We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill--Noether rank of a tropical curve. We recall Coppens' counterexample of Martens-special chain of cycles, and we generalize the construction defining another class of graphs, Martens-special trees of cycles, for which the conjecture does not hold in a similar setting. These are not the only counterexamples. However, we prove that the conjecture holds for all metric graphs with a stricter assumption on the degree in the Brill--Noether rank. |
| title | A tropical version of Martens' theorem for metric graphs |
| topic | Combinatorics Algebraic Geometry 05C25, 14T15 |
| url | https://arxiv.org/abs/2512.13208 |