{
  "id": "1908.05988",
  "version": "v1",
  "published": "2019-08-16T14:27:43.000Z",
  "updated": "2019-08-16T14:27:43.000Z",
  "title": "Higher Connectivity of Tropicalizations",
  "authors": [
    "Diane Maclagan",
    "Josephine Yu"
  ],
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0is (d-l)-connected through codimension one, where l is the dimension of the lineality space of the tropicalization. From this we obtain a higher connectivity result for skeleta of rational polytopes. We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-16T14:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14T05"
    ],
    "keywords": [
      "tropicalization",
      "irreducible variety",
      "higher connectivity result",
      "bertini theorem",
      "generic hyperplane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}