Newton–Okounkov Polytopes of Type \(A\) Flag Varieties of Small Ranks Arising from Cluster Structures

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发表日期：

2024年9月1日

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Yunhyung Cho,
Naoki Fujita,
Akihiro Higashitani,
Eunjeong Lee

摘要

Abstract

A flag variety is a smooth projective homogeneous variety. In this paper, we study Newton–Okounkov polytopes of the flag variety \(\mathrm{Fl}(\mathbb C^4)\) arising from its cluster structure. More precisely, we present defining inequalities of such Newton–Okounkov polytopes of \(\mathrm{Fl}(\mathbb C^4)\) . Moreover, we classify these polytopes, establishing their equivalence under unimodular transformations.