{
  "id": "2310.06477",
  "version": "v1",
  "published": "2023-10-10T09:47:07.000Z",
  "updated": "2023-10-10T09:47:07.000Z",
  "title": "Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures",
  "authors": [
    "Yunhyung Cho",
    "Naoki Fujita",
    "Akihiro Higashitani",
    "Eunjeong Lee"
  ],
  "categories": [
    "math.AG",
    "math.CO",
    "math.RT"
  ],
  "abstract": "A flag variety is a smooth projective homogeneous variety. In this paper, we study Newton-Okounkov polytopes of the flag variety $Fl(\\mathbb{C}^4)$ arising from its cluster structure. More precisely, we present defining inequalities of such Newton-Okounkov polytopes of $Fl(\\mathbb{C}^4)$. Moreover, we classify these polytopes, establishing their equivalence under unimodular transformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-10T09:47:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "05E10",
      "14M25",
      "13F60"
    ],
    "keywords": [
      "flag variety",
      "cluster structure",
      "small ranks arising",
      "study newton-okounkov polytopes",
      "smooth projective homogeneous variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}