Row Convex Tableaux and Bott-Samelson Varieties
Philip Foth, Sangjib Kim

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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry
