Newton-okounkov polytopes of schubert varieties arising from cluster structures

Naoki Fujita, Hironori Oya

Research output: Contribution to journalArticlepeer-review


The theory of Newton-Okounkov bodies is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of projective varieties. In this paper, we study Newton-Okounkov bodies of Schubert varieties from the theory of cluster algebras. We construct Newton-Okounkov bodies using specific valuations which generalize extended g-vectors in cluster theory, and discuss how these bodies are related to string polytopes and Nakashima-Zelevinsky polytopes.

MSC Codes 05E10 (Primary) 13F60, 14M15, 14M25, 52B20 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Feb 23


  • Cluster algebra
  • Nakashima-Zelevinsky polytope
  • Newton-Okounkov body
  • String polytope
  • Toric degeneration

ASJC Scopus subject areas

  • General

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