Automorphism Groups on Tropical Curves: Some Cohomology Calculations

Details Automorphism Groups on Tropical Curves: Some Cohomology Calculations Automorphism Groups on Tropical Curves: Some Cohomology Calculations

2010-06-24

arxiv.org/abs/1006.4869v2

Mathematics

Algebraic Geometry

17 pages. Comments welcome. Version 2: plugged a small leak in the proof of Prop.1, section 5; fixed typos and added an acknow

Scientific paper

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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