5 papers
Tropical curves with parallel rays
JuAe Song
In the previous works, the rational function semifields of abstract tropical curves were characterized. In this paper, we give a contravariant categorical equivalence between the c…
Tropical function fields, finite generation, and faithful tropicalization
Omid Amini, Shu Kawaguchi, JuAe Song
Given an algebraic variety defined over a discrete valuation field and a skeleton of its Berkovich analytification, the tropicalization process transforms function field of the var…
A geometric interpretation of Krull dimensions of -algebras
JuAe Song, Yasuhito Nakajima
We investigate Krull dimensions of semirings and semifields dealt in tropical geometry. For a congruence on a tropical Laurent polynomial semiring $\boldsymbol{T}[X_1^{\pm}, \l…
Finitely generated congruences on tropical rational function semifields
JuAe Song
We prove that the congruence on the tropical rational function semifield in -variables associated with a subset of is finitely generated if and only if th…
Congruences on tropical rational function semifields and tropical curves
JuAe Song
We define tropical rational function semifields and prove that a tropical curve is realized (except for points at infinity…