Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910458688045056 |
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| author | Kowaki, Nobukazu |
| author_facet | Kowaki, Nobukazu |
| contents | A sequence of combinatorial mutations of matching field polytopes preserves the property of giving rise to a toric degeneration of Grassmannians. In this paper, we find a way to check that two matching field polytopes are combinatorial mutation equivalence using tropical hyperplane arrangements, ``literally at a glance". Our way can prove that block diagonal matching fields are combinatorial mutations equivalent to diagonal matching fields. This is one of main results in \cite{clarke2021combinatorial}. Our result can be regarded as a generalization of that result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians Kowaki, Nobukazu Combinatorics Algebraic Geometry Primary:14M15, Secondary, 13F65, 13P10 A sequence of combinatorial mutations of matching field polytopes preserves the property of giving rise to a toric degeneration of Grassmannians. In this paper, we find a way to check that two matching field polytopes are combinatorial mutation equivalence using tropical hyperplane arrangements, ``literally at a glance". Our way can prove that block diagonal matching fields are combinatorial mutations equivalent to diagonal matching fields. This is one of main results in \cite{clarke2021combinatorial}. Our result can be regarded as a generalization of that result. |
| title | Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians |
| topic | Combinatorics Algebraic Geometry Primary:14M15, Secondary, 13F65, 13P10 |
| url | https://arxiv.org/abs/2405.15215 |