On torsion in the intersection cohomology of Schubert varieties

TL;DR

This paper demonstrates that prime torsion in the local intersection cohomology of Schubert varieties grows exponentially with rank, using geometric methods involving singular points and Euler classes.

Contribution

It provides a geometric proof showing exponential growth of prime torsion in intersection cohomology, complementing previous algebraic approaches.

Findings

Prime torsion grows exponentially with rank.

Identification of highly singular points in Schubert varieties.

Calculation of Euler classes in Bott-Samelson resolutions.

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.