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arXiv · 2501.03903

Tropical trigonal curves

Margarida Melo·Angelina Zheng
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Abstract

We prove that the existence of a divisor of degree $3$ and Baker-Norine rank at least $1$ on a $3$-edge connected tropical curve is equivalent to the existence of a non-degenerate harmonic morphism of degree $3$ from a tropical modification of it to a tropical rational curve. Using the second description, we define the moduli spaces of $3$-edge connected tropical trigonal covers and of $3$-edge connected tropical trigonal curves, the latter as a locus in the moduli space of tropical curves. Finally, we prove that the moduli space of $3$-edge connected genus $g$ tropical trigonal curves has the same dimension as the moduli space of genus $g$ algebraic trigonal curves.

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Margarida Melo, Angelina Zheng. 2025-01-07. Tropical trigonal curves. https://doi.org/10.5802/alco.465

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