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Hokkaido University Preprint Series in Mathematics >
Hilbert schemes and simple singularities An and Dn
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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