Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians

Nobukazu Kowaki

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arXiv · 2405.15215

Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians

Nobukazu Kowaki

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Abstract

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.

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Nobukazu Kowaki. 2024-05-24. Tropical hyperplane arrangements and combinatorial mutations of the matching field polytopes of Grassmannians. https://arxiv.org/abs/2405.15215

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