Partial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties

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dc.creatorKaledin, D.
dc.creatorVerbitsky, M.
dc.date1998-12-14
dc.date.accessioned2026-07-07T05:27:13Z
dc.date.available2026-07-07T05:27:13Z
dc.descriptionWe study the partial resolutions of singularities related to Hilbert schemes of points on an affine space. Consider a quotient of a vector space $V$ by an action of a finite group $G$ of linear transforms. Under some additional assumptions, we prove that the partial desingularization of Hilbert type is smooth only if the action of $G$ is generated by complex reflections. This is used to study the subvarieties of a Hilbert scheme of a complex torus. We show that any subvariety of a generic deformation of a Hilbert scheme of a torus is birational to a quotient of another torus by an action of a Weyl group of some semisimple Lie algebra. In Appendix, we produce counterexamples to a false theorem stated in our preprint math.AG/9801038.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/9812078
dc.identifierhttp://arxiv.org/abs/math/9812078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77842
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subjectDifferential Geometry
dc.subjectRepresentation Theory
dc.titlePartial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties
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