On hypersurface quotient singularities of dimension 4
We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n≥4 through the theory of Hilbert scheme of group orbits. For a linear special group G acting on ℂn, we study the G-Hilbert scheme HilbG(ℂn) and crepant resolutions of ℂn/G for G the A-type abelian group Ar(n). For n=...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204302140 |
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| Summary: | We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension n≥4 through the theory of Hilbert scheme of group orbits. For a linear special group G acting on ℂn, we study the G-Hilbert scheme HilbG(ℂn) and crepant resolutions of ℂn/G for G the A-type abelian group Ar(n). For n=4, we obtain the explicit structure of HilbAr(4)(ℂ4). The crepant resolutions of ℂ4/Ar(4) are constructed through their relation with HilbAr(4)(ℂ4), and the connections between these crepant resolutions are found by the flop procedure of 4-folds. We also make some primitive discussion on HilbG(ℂn) for G the alternating group 𝔄n+1 of degree n+1 with the standard representation on ℂn; the detailed structure of Hilb𝔄4(ℂ3) is explicitly constructed. |
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| ISSN: | 0161-1712 1687-0425 |