Newton-Okounkov polytopes of Schubert varieties arising from cluster structures

2020/02/23 by Naoki Fujita, Fujita, Naoki, Hironori Oya +1 · 1 citation
Mathematics · Physics and Astronomy · #05E10 (Primary) 13F60 #14M15 #14M25 #52B20 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2002.09912

openalex publication_date 2020/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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• Semi-toric degenerations of Richardson varieties arising from cluster structures on flag varieties

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