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arXiv · 2310.06477

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

Yunhyung Cho·Naoki Fujita·Akihiro Higashitani·Eunjeong Lee
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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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Yunhyung Cho, Naoki Fujita, Akihiro Higashitani, Eunjeong Lee. 2023-10-10. Newton-Okounkov polytopes of type $A$ flag varieties of small ranks arising from cluster structures. https://arxiv.org/abs/2310.06477

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