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arxiv: 1006.4869 · v2 · pith:TBBS3WXYnew · submitted 2010-06-24 · 🧮 math.AG

Automorphism Groups on Tropical Curves: Some Cohomology Calculations

David Joyner , Amy Ksir , Caroline Grant Melles This is my paper
classification 🧮 math.AG
keywords tropicalabstractautomorphismclasscurvesdivisorequivalenceinvariant
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Let $X$ be an abstract tropical curve and let $G$ be a finite subgroup of the automorphism group of $X$. Let $D$ be a divisor on $X$ whose equivalence class is $G$-invariant. We address the following question: is there always a divisor $D'$ in the equivalence class of $D$ which is $G$-invariant? Our main result is that the answer is "yes" for all abstract tropical curves. A key step in our proof is a tropical analogue of Hilbert's Theorem 90.

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Cited by 1 Pith paper

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  1. The Tropical Moduli Space of Degree-3 Rational Maps

    math.AG 2026-05 unverdicted novelty 7.0

    The authors classify all degree-3 tropical rational maps into exactly ten combinatorial types and build a polyhedral model of their moduli space parametrized by gap lengths between breakpoints.