From moment graphs to intersection cohomology

Abstract

We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our formula applies includes Schubert varieties in flag varieties and affine flag varieties. We also prove a monotonicity result on local intersection cohomology stalks.

20 pages, 1 figure