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Hilbert schemes and simple singularities An and Dn

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83494

Title: Hilbert schemes and simple singularities An and Dn
Authors: Ito, Y. Browse this author
Nakamura, I. Browse this author
Issue Date: 1-Sep-1996
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 348
Start Page: 1
End Page: 22
Abstract: For any finite subgroup G of SL(2, C) of order n, we consider a certain subscheme HilbG(A2 ) of Hilbn(A2 ) consisting of G-invariant 0-dimensional subschemes of length n. We prove without using the classification of finite subgroups in SL(2,C) that HilbG(A2 ) is a minimal resolution of a simple singularity A2 /G in the canonical manner. Any point of the exceptional set is a G-invariant 0-dimensional subscheme of A2 with support the origin, to which we associate the ideal sheaf I defining the subscheme. A minimal G-submodule of I generating the O A2-module I is a one dimensional trivial G-module plus one or two nontrivial mutually distinct irreducible G-modules. This gives a bijective correpondence between the set of all the irreducible components of the exceptional set and the set of all the equivalence classes of irreducible G-modules, which turns out to be the ( classical) McKay correspondence.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69098
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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