Row Convex Tableaux and Bott-Samelson Varieties

TL;DR

This paper explores the algebraic structure of Bott-Samelson varieties using row convex tableaux, establishing bases, deformations, and degenerations, and providing explicit computations for a specific three-dimensional case.

Contribution

It introduces a novel approach using row convex tableaux to analyze section rings and provides detailed computations for a particular Bott-Samelson variety.

Findings

Established flat deformations of section rings

Constructed standard monomial bases

Computed Hilbert polynomial and toric degenerations for a specific variety

Abstract

By using row convex tableaux, we study the section rings of Bott-Samelson varieties of type A. We obtain flat deformations and standard monomial type bases of the section rings. In a separate section, we investigate a three dimensional Bott-Samelson variety in detail and compute its Hilbert polynomial and toric degenerations.