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<p>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 equivalent using tropical hyperplane arrangements, “literally at a glance”. Our method can prove that block diagonal matching fields are combinatorial mutation equivalent to diagonal matching fields. So our results provide a simpler proof of a result of Clarke, Higashitani, and Mohammadi.</p>

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

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Nobukazu Kowaki

摘要

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 equivalent using tropical hyperplane arrangements, “literally at a glance”. Our method can prove that block diagonal matching fields are combinatorial mutation equivalent to diagonal matching fields. So our results provide a simpler proof of a result of Clarke, Higashitani, and Mohammadi.