Work

A tropical version of Martens' theorem for metric graphs

Year: 2026

Type: article

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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70505

Authors: Giusi Capobianco, Angelina Zheng

Institutions: University of Rome Tor Vergata, University of Tübingen

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Alexander von Humboldt-Stiftung, Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni