Automorphism Groups on Tropical Curves: Some Cohomology Calculations
David Joyner, Amy Ksir, and Caroline Grant Melles

TL;DR
This paper proves that for any finite automorphism group acting on an abstract tropical curve, there always exists a G-invariant divisor within a G-invariant divisor class, using a tropical analogue of Hilbert's Theorem 90.
Contribution
It establishes the existence of G-invariant divisors in G-invariant classes on tropical curves, introducing a tropical version of Hilbert's Theorem 90.
Findings
Existence of G-invariant divisors on tropical curves proven.
Development of a tropical analogue of Hilbert's Theorem 90.
Applicable to all abstract tropical curves.
Abstract
Let be an abstract tropical curve and let be a finite subgroup of the automorphism group of . Let be a divisor on whose equivalence class is -invariant. We address the following question: is there always a divisor in the equivalence class of which is -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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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications
