Quadratic Gr\"obner bases of block diagonal matching field ideals and toric degenerations of Grassmannians

TL;DR

This paper proves that certain toric ideals associated with block diagonal matching fields have quadratic Gr"obner bases, leading to new toric degenerations of Grassmannians, which enhances understanding of their algebraic and geometric structures.

Contribution

It establishes quadratic Gr"obner bases for specific toric ideals and introduces new toric degenerations of Grassmannians, expanding the toolkit for studying their algebraic properties.

Findings

Toric ideals of s-block diagonal matching fields have quadratic Gr"obner bases.

These ideals are quadratically generated.

New families of toric degenerations of Grassmannians are constructed.

Abstract

In the present paper, we prove that the toric ideals of certain $s$-block diagonal matching fields have quadratic Gr\"obner bases. Thus, in particular, those are quadratically generated. By using this result, we provide a new family of toric degenerations of Grassmannians.