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arXiv:2310.06477 [math.AG]AbstractReferencesReviewsResources

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

Yunhyung Cho, Naoki Fujita, Akihiro Higashitani, Eunjeong Lee

Published 2023-10-10Version 1

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.

Categories: math.AG, math.CO, math.RT
Subjects: 14M15, 05E10, 14M25, 13F60
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