New kinds of block diagonal matching fields and toric degenerations of Grassmannians

2025/05/01 by Higashitani, Akihiro, Kowaki, Nobukazu
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.00388

Abstract

Block diagonal matching field has many previous works. In general, a coherent matching field induces a monomial order to Plücker 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.

Citations

• Quadratic Gr "obner bases of block diagonal matching field ideals and\n toric degenerations of Grassmannians
• Combinatorial Mutations and Block Diagonal Polytopes
• Maximal Minors and Their Leading Terms

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• Quadratic Gr "obner bases of block diagonal matching field ideals and\n toric degenerations of Grassmannians
• Combinatorial Mutations and Block Diagonal Polytopes
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