2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77842We 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/9801038.33 pagesAlgebraic GeometryComplex VariablesDifferential GeometryRepresentation Theorytext