Row Convex Tableaux and Bott–samelson varieties

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.

Standard Monomial Theory of RR Varieties

“…[6, p. 281] and [2, Theorem 1.2])). Using this method, [3] shows that Z i can be flatly deformed into a toric variety. For Z j , we will apply an analogous method to the quotient algebra R j,m = R i,m / ker Φ.…”