Tropical trigonal curves: the general case

Margarida Melo; Angelina Zheng

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arXiv · 2509.09502

Tropical trigonal curves: the general case

Margarida Melo·Angelina Zheng

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Abstract

This paper is a follow-up of a previous work in which we show that, for a $3$-edge connected tropical curve $\Gamma$, the existence of a divisor of degree $3$ and Baker-Norine rank at least $1$ in $\Gamma$ is equivalent to the existence of a non-degenerate harmonic morphism of degree $3$ from a tropical modification of $\Gamma$ to a tropical rational curve. In this work, we extend this result to a tropical curve with lower edge connectivity which does not contain a cycle of (at least three) separating vertices (a so-called necklace).

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Margarida Melo, Angelina Zheng. 2025-09-11. Tropical trigonal curves: the general case. https://arxiv.org/abs/2509.09502

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