The Tropical Moduli Space of Degree-3 Rational Maps
Algebraic Geometry
2026-05-18 v1 Combinatorics
Abstract
We construct and study the tropical moduli space of degree- tropical rational maps up to post-composition. Using a combinatorial description in terms of slope sequences, we classify all such maps and show that there are exactly ten combinatorial types. This yields a polyhedral model of parametrized by gap lengths between break points. We determine the automorphism groups and obtain a stratification by explicit linear conditions. We also relate the construction to tropical Hurwitz theory and describe a natural compactification via degenerations of the parameters.
Keywords
Cite
@article{arxiv.2605.15347,
title = {The Tropical Moduli Space of Degree-3 Rational Maps},
author = {Tony Shaska and Mohammad-Reza Siadat},
journal= {arXiv preprint arXiv:2605.15347},
year = {2026}
}