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arXiv · 1006.4869

Automorphism Groups on Tropical Curves: Some Cohomology Calculations

David Joyner·Amy Ksir·Caroline Grant Melles
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Abstract

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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David Joyner, Amy Ksir, Caroline Grant Melles. 2010-06-24. Automorphism Groups on Tropical Curves: Some Cohomology Calculations. https://arxiv.org/abs/1006.4869

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