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Partial resolutions of nilpotent varieties. (English) Zbl 0576.14046
Astérisque 101-102, 23-74 (1983).
The authors generalize the Springer resolution of singularities $$\pi$$ : $$\tilde {\mathcal N}\to {\mathcal N}$$ for the variety $${\mathcal N}$$ of nilpotent matrices in GL(n,$${\mathbb{C}})$$, by using the variety of partial flags $${\mathcal P}_ p$$. This gives the ”partial resolutions” $${\mathcal N}^ p\to {\mathcal N}$$ for general reductive groups. Then, the authors use them in the analysis of the topology of singularities of $${\mathcal N}$$ by means of intersection homologies and Springer’s theory of Weyl group representations.
For the entire collection see [Zbl 0515.00021].
Reviewer: S.Priščepionok

##### MSC:
 14L30 Group actions on varieties or schemes (quotients) 22E25 Nilpotent and solvable Lie groups 14E15 Global theory and resolution of singularities (algebro-geometric aspects) 14M17 Homogeneous spaces and generalizations 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry