{
  "id": "1902.00891",
  "version": "v1",
  "published": "2019-02-03T13:22:38.000Z",
  "updated": "2019-02-03T13:22:38.000Z",
  "title": "Classification of triples of lattice polytopes with a given mixed volume",
  "authors": [
    "Gennadiy Averkov",
    "Christopher Borger",
    "Ivan Soprunov"
  ],
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We present an algorithm for the classification of triples of lattice polytopes with a given mixed volume $m$ in dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number of which is finite for fixed $m$. Following this algorithm, we enumerate all irreducible triples of normalized mixed volume up to 4 that are inclusion-maximal. This produces a classification of generic trivariate sparse polynomial systems with up to 4 solutions in the complex torus, up to monomial changes of variables. By a recent result of Esterov, this leads to a description of all generic trivariate sparse polynomial systems that are solvable by radicals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-03T13:22:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "52B20",
      "52A39",
      "52A38",
      "52B10"
    ],
    "keywords": [
      "mixed volume",
      "lattice polytopes",
      "generic trivariate sparse polynomial systems",
      "classification",
      "irreducible triples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}