Small resolutions of singularities of Schubert varieties. (English. Russian original) Zbl 0559.14006
Funct. Anal. Appl. 17, 142-144 (1983); translation from Funkts. Anal. Prilozh. 17, No. 2, 75-77 (1983).
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.
Reviewer: H.Esnault
MSC:
| 14E15 | Global theory and resolution of singularities (algebro-geometric aspects) |
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 14F99 | (Co)homology theory in algebraic geometry |
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