Allen Knutson (Jan. 28, 2022):  Resolutions of Richardson varieties, stable curves, and ...
Channel: Algebraic Geometry at Stanford
Date: 2022-01-29

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

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 each case the dual simplicial complex is actually homeomorphic to a sphere.