{"paper":{"title":"Tropical curves with parallel rays","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Abstract tropical curves can now include parallel rays while maintaining a categorical equivalence to their rational function semifields.","cross_cats":[],"primary_cat":"math.AG","authors_text":"JuAe Song","submitted_at":"2026-05-16T09:50:20Z","abstract_excerpt":"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 category of abstract tropical curves with morphisms and the category of semifields over the tropical semifield $\\boldsymbol{T}$ characterized above with $\\boldsymbol{T}$-algebra homomorphisms.\n  The characterization tells us that the traditional definition of abstract tropical curves has a fatal flaw such that we are never able to deal with parallel rays, unlike the traditional tropical curves, which generally admit t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce a new notion of abstract tropical curves with parallel rays. 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