Automorphism Groups on Tropical Curves: Some Cohomology Calculations

David Joyner; Amy Ksir; Caroline Grant Melles

Automorphism Groups on Tropical Curves: Some Cohomology Calculations

Algebraic Geometry 2010-10-20 v2

Authors: David Joyner , Amy Ksir , Caroline Grant Melles

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.

Keywords

tropical curves automorphism groups divisors cohomology Hilbert's Theorem 90 G-invariant

Cite

@article{arxiv.1006.4869,
  title  = {Automorphism Groups on Tropical Curves: Some Cohomology Calculations},
  author = {David Joyner and Amy Ksir and Caroline Grant Melles},
  journal= {arXiv preprint arXiv:1006.4869},
  year   = {2010}
}

Comments

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

Automorphism Groups on Tropical Curves: Some Cohomology Calculations

Abstract

Keywords

Cite

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