# Resolutions of Richardson varieties, stable curves, and dual simplicial spheres

## Location

The combinatorics of a simple normal crossings divisor determines a "dual" simplicial complex. Kollár and Xu showed that when this divisor is anticanonical, the simplicial complex has the rational homology of a sphere. I'll construct two resolutions-of-singularities of Richardson varieties (a slight generalization of Schubert varieties), one using Bott-Samelson manifolds, the other (requiring no choices!) using circle-equivariant stable curves. In both cases the dual simplicial complex is actually **homeomorphic to** a sphere.

The synchronous discussion for Allen Knutson’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2022-01-28-ak (and will be deleted after ~3-7 days).