2025/01/07 by Melo, Margarida, Zheng, Angelina
#14T05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.03903
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.