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arXiv · 2403.09959

Poset polytopes and pipe dreams: toric degenerations and beyond

Ievgen Makedonskyi·Igor Makhlin
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Abstract

We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for marked chain-order polytopes of Dynkin types A and C. These toric degenerations also give rise to further algebraic and geometric objects such as PBW-monomial bases and Newton--Okounkov bodies. We discuss a construction of the former in the type A case and of the latter in type C.

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Ievgen Makedonskyi, Igor Makhlin. 2024-03-15. Poset polytopes and pipe dreams: toric degenerations and beyond. https://arxiv.org/abs/2403.09959

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