Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial resolutions of Hilbert type, Dynkin diagrams, and generalized
  Kummer varieties   We 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.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol