{
  "id": "2403.09959",
  "version": "v1",
  "published": "2024-03-15T01:50:09.000Z",
  "updated": "2024-03-15T01:50:09.000Z",
  "title": "Poset polytopes and pipe dreams: toric degenerations and beyond",
  "authors": [
    "Ievgen Makedonskyi",
    "Igor Makhlin"
  ],
  "comment": "Extended abstract for FPSAC 2024",
  "categories": [
    "math.AG",
    "math.CO",
    "math.RT"
  ],
  "abstract": "We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for marked chain-order polytopes of Dynkin types A and C. These toric degenerations also give rise to further algebraic and geometric objects such as PBW-monomial bases and Newton--Okounkov bodies. We discuss a construction of the former in the type A case and of the latter in type C.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-15T01:50:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poset polytopes",
      "pipe dreams",
      "produce toric degenerations",
      "newton-okounkov bodies",
      "marked chain-order polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}