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

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arxiv 2310.06477 v1 pith:B5KSZ7T3 submitted 2023-10-10 math.AG math.COmath.RT

Yunhyung Cho , Naoki Fujita , Akihiro Higashitani , Eunjeong Lee This is my paper
classification math.AGmath.COmath.RT
keywords polytopesflagnewton-okounkovvarietyarisingclustermathbbclassify
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abstract

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.

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