{
  "id": "1006.4869",
  "version": "v2",
  "published": "2010-06-24T20:11:51.000Z",
  "updated": "2010-10-18T21:30:35.000Z",
  "title": "Automorphism Groups on Tropical Curves: Some Cohomology Calculations",
  "authors": [
    "David Joyner",
    "Amy Ksir",
    "Caroline Grant Melles"
  ],
  "comment": "17 pages. Comments welcome. Version 2: plugged a small leak in the proof of Prop.1, section 5; fixed typos and added an acknowledgement",
  "categories": [
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-10-18T21:30:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14T05",
      "14H37"
    ],
    "keywords": [
      "automorphism group",
      "cohomology calculations",
      "abstract tropical curve",
      "equivalence class",
      "finite subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.4869J"
    }
  }
}