Toric degenerations of Grassmannians from matching fields

Abstract

We study the algebraic combinatorics of monomial degenerations of Plücker forms which is governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a necessary condition for a matching field to yield a Khovanskii basis of the Plücker algebra for $3$-planes in $n$-space. When the ideal associated to the matching field is quadratically generated this condition is both necessary and sufficient. Finally, we describe a family of matching fields, called $2$-block diagonal, whose ideals are quadratically generated. These matching fields produce a new family of toric degenerations of $\Gr(3, n)$.

Cited by in corpus (4)

• Toric degenerations of Grassmannians and Schubert varieties from matching field tableaux
• Toric degenerations of partial flag varieties and combinatorial mutations of matching field polytopes
• Matching fields and lattice points of simplices
• Minimal cellular resolutions of powers of matching field ideals