Geodesic
Newton–Okounkov Polytopes of Type $A$ Flag Varieties of Small Ranks Arising from Cluster Structures
Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 382-397 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: flag varieties, Newton–Okounkov bodies, cluster algebras, toric varieties. 
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     author = {Yunhyung Cho and Naoki Fujita and Akihiro Higashitani and Eunjeong Lee},
     title = {Newton{\textendash}Okounkov {Polytopes} of {Type} $A$ {Flag} {Varieties} of {Small} {Ranks} {Arising} from {Cluster} {Structures}},
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Yunhyung Cho; Naoki Fujita; Akihiro Higashitani; Eunjeong Lee. Newton–Okounkov Polytopes of Type $A$ Flag Varieties of Small Ranks Arising from Cluster Structures. Informatics and Automation, Topology, Geometry, Combinatorics, and Mathematical Physics, Tome 326 (2024), pp. 382-397. http://geodesic.mathdoc.fr/item/TRSPY_2024_326_a16/

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