Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures

Akihiro Higashitani; Eunjeong Lee; Naoki Fujita; Yunhyung Cho

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Newton-Okounkov polytopes of type A flag varieties of small ranks arising from cluster structures

Yunhyung Cho , Naoki Fujita , Akihiro Higashitani , Eunjeong Lee This is my paper

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keywords polytopesflagnewton-okounkovvarietyarisingclustermathbbclassify

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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 $Fl(\mathbb{C}^4)$ arising from its cluster structure. More precisely, we present defining inequalities of such Newton-Okounkov polytopes of $Fl(\mathbb{C}^4)$. Moreover, we classify these polytopes, establishing their equivalence under unimodular transformations.

Newton-Okounkov polytopes of type A flag varieties of small ranks arising from cluster structures

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