On torsion in the intersection cohomology of Schubert varieties

2015/12/28 by Williamson, Geordie
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1512.08295

Abstract

We prove that the prime torsion in the local integral intersection cohomology of Schubert varieties in the flag variety of the general linear group grows exponentially in the rank. The idea of the proof is to find a highly singular point in a Schubert variety and calculate the Euler class of the normal bundle to the (miraculously smooth) fibre in a particular Bott-Samelson resolution. The result is a geometric version of an earlier result established using Soergel bimodule techniques.

Related

• A study of intersections of Schubert varieties
• On the cohomology rings of real flag manifolds: Schubert cycles
• Schubert calculus and torsion explosion
• An analogue of Bott's theorem for Schubert varieties-related to torus semistable points
• Introduction to the Cohomology of the Flag Variety