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New kinds of block diagonal matching fields and toric degenerations of Grassmannians (2505.00388v1)
Published 1 May 2025 in math.CO and math.AC
Abstract: Block diagonal matching field has many previous works. In general, a coherent matching field induces a monomial order to Pl\"{u}cker algebra, and block diagonal matching fields are a kind of coherent matching fields. In the present paper, we introduce a new kind of block diagonal matching fields and study the problem when they give a SAGBI basis. As a corollary, we provide a new family of toric degenerations of Grassmannians by using SAGBI bases.
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