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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