Small resolutions of singularities of Schubert varieties (Q802614)

The explicit computation of the intersection cohomology IH(X) à la Goresky-MacPherson of a complex space X is usually difficult. Nevertheless, according to Goresky-MacPherson, if a small resolution of the singularities \(\tilde X\to X\) of X exists, then IH(X) is roughly speaking the same as the cohomology \(H(\tilde X)\) of \(\tilde X.\) The author proves by an explicit construction the existence of a small resolution for any Schubert cell and therefore obtains a combinatorial description of the intersection cohomology.