Tropical trigonal curves

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.

v3: updated to match the published version

References in corpus (6)

• The tropicalization of the moduli space of curves
• Chip-firing games, potential theory on graphs, and spanning trees
• Tropical curves, graph complexes, and top weight cohomology of M_g
• Lifting harmonic morphisms II: tropical curves and metrized complexes
• Tropical moduli spaces as symmetric Delta-complexes
• Hyperelliptic graphs and metrized complexes