Toric Degeneration of Bott-Samelson-Demazure-Hansen varieties

Abstract

In this paper we construct a degeneration of Bott-Samelson-Demazure-Hansen varieties to toric varieties in an algebraic family and study the geometry of the resulting toric varieties. We give a natural set of torus invariant curves that generate the Chow group of $1$-cycles of the limiting toric variety and express the ample cone of this toric variety as a sub-cone of the ample cone of the corresponding Bott-Samelson-Demazure-Hansen variety. We also give a description of Extremal and Mori rays and determine when this toric variety is Fano.

Cited by in corpus (2)

• A note on toric degeneration of a Bott-Samelson-Demazure-Hansen variety
• Deformation of Bott-Samelson varieties and variations of isotropy structures