Poset polytopes and pipe dreams: toric degenerations and beyond
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914715442085888 |
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| author | Makedonskyi, Ievgen Makhlin, Igor |
| author_facet | Makedonskyi, Ievgen Makhlin, Igor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09959 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poset polytopes and pipe dreams: toric degenerations and beyond Makedonskyi, Ievgen Makhlin, Igor Algebraic Geometry Combinatorics Representation Theory 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. |
| title | Poset polytopes and pipe dreams: toric degenerations and beyond |
| topic | Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2403.09959 |