International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 48, Pages 2547-2581
On hypersurface quotient singularities of dimension
Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan
Received 18 February 2003
Copyright © 2004 Li Chiang and Shi-Shyr Roan. 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 consider geometrical problems on Gorenstein hypersurface orbifolds of dimension through the theory of Hilbert scheme of group orbits. For a linear special group acting on , we study the -Hilbert scheme and crepant resolutions of for the -type abelian group . For , we obtain the explicit structure of . The crepant resolutions of are constructed through their relation with , and the connections between these crepant resolutions are found by the flop procedure of 4-folds. We also make some primitive discussion on for the alternating group of degree with the standard representation on ; the detailed structure of is explicitly constructed.