Bulletin of the London Mathematical Society· 2026Q1
A tropical version of Martens' theorem for metric graphs
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- 2026year
Short summary
A new class of counterexamples, Martens-special trees of cycles, is constructed for a tropical version of Martens' theorem, but the theorem is proven to hold for metric graphs with a stricter degree assumption in the Brill-Noether rank.
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Key points
- A new class of counterexamples, Martens-special trees of cycles, is constructed for a tropical version of Martens' theorem.
- The study recalls Coppens' prior counterexample of Martens-special chain of cycles.
- The conjecture is proven to hold for metric graphs under a stricter assumption on the degree in the Brill-Noether rank.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract 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.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science