{
  "id": "2403.14389",
  "version": "v1",
  "published": "2024-03-21T13:29:44.000Z",
  "updated": "2024-03-21T13:29:44.000Z",
  "title": "On the Weights of Root Subgroups of Affine Toric Varieties",
  "authors": [
    "Immanuel van Santen"
  ],
  "comment": "22 pages, comments are welcome! arXiv admin note: substantial text overlap with arXiv:2112.04784",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "Let $X$ be an affine toric variety and let $D(X)$ be the set of weights of all root subgroups. It is known that $D(X)$ together with its embedding into the character group determines $X$ as a toric variety. In this article we prove that $X$ is already determined by the abstract set $D(X)$ together with some additional combinatorial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-21T13:29:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14R20",
      "14M25"
    ],
    "keywords": [
      "affine toric variety",
      "root subgroups",
      "additional combinatorial data",
      "character group determines",
      "abstract set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}