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

TL;DR

This paper introduces a new class of block diagonal matching fields and explores their role in generating SAGBI bases, leading to new toric degenerations of Grassmannians, advancing algebraic and geometric understanding.

Contribution

It presents a novel type of block diagonal matching fields and analyzes their capacity to produce SAGBI bases for Grassmannians.

Findings

New block diagonal matching fields constructed

Identification of conditions for SAGBI basis formation

Development of new toric degenerations of Grassmannians

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.