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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 11, Pages 649-669

Orbifolds and finite group representations

Institute of Mathematics, Academia Sinica, Taipei, Taiwan

Received 12 December 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian group Ar(n) for A-type hypersurface quotient singularity of dimension n is introduced. For n=4, the structure of Hilbert scheme of group orbits and crepant resolutions of Ar(4)-singularity are obtained. The flop procedure of 4-folds is explicitly constructed through the process.