From standard monomial theory to semi-toric degenerations via Newton-Okounkov bodies

TL;DR

This paper explores how Hodge algebra structures induce semi-toric degenerations of Grassmann varieties through the use of quasi-valuations and Newton-Okounkov body triangulations.

Contribution

It introduces a novel method to construct semi-toric degenerations using quasi-valuations and Newton-Okounkov bodies, linking algebraic and geometric structures.

Findings

Semi-toric degenerations constructed for Grassmann varieties.

Use of quasi-valuations to realize degenerations.

Triangulations of Newton-Okounkov bodies facilitate the process.

Abstract

The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-toric degenerations using quasi-valuations and triangulations of Newton-Okounkov bodies.