{
  "id": "2301.02545",
  "version": "v1",
  "published": "2023-01-06T14:55:51.000Z",
  "updated": "2023-01-06T14:55:51.000Z",
  "title": "A survey on toric degenerations of projective varieties",
  "authors": [
    "Lara Bossinger"
  ],
  "comment": "I wrote this survey for the Proceedings of the Nottingham Algebraic Geometry Seminar in 2021. I hope it serves as an overview or introduction to Toric Degenerations, it is especially addressed to students and non experts. Comments are very welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this survey I summarize the constructions of toric degenerations obtained from valuations and Gr\\\"obner theory and describe in which sense they are equivalent. I show how adapted bases can be used to generalize the classical Newton polytope to what is called a $\\mathbb B$-Newton polytope. The $\\mathbb B$-Newton polytope determines the Newton--Okounkov polytopes of all Khovanskii-finite valuations sharing the adapted standard monomial basis $\\mathbb B$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-06T14:55:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25",
      "13P10",
      "14T05"
    ],
    "keywords": [
      "toric degenerations",
      "projective varieties",
      "adapted standard monomial basis",
      "newton polytope determines",
      "classical newton polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}