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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| Format: | Article |
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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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| author | Li Chiang Shi-Shyr Roan |
| author_facet | Li Chiang Shi-Shyr Roan |
| author_sort | Li Chiang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-197f4c30f65645119aa025ec9ecd9c96 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-197f4c30f65645119aa025ec9ecd9c962025-02-03T06:06:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004482547258110.1155/S0161171204302140On hypersurface quotient singularities of dimension 4Li Chiang0Shi-Shyr Roan1Institute of Mathematics, Academia Sinica, Taipei 11529, TaiwanInstitute of Mathematics, Academia Sinica, Taipei 11529, TaiwanWe 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.http://dx.doi.org/10.1155/S0161171204302140 |
| spellingShingle | Li Chiang Shi-Shyr Roan On hypersurface quotient singularities of dimension 4 International Journal of Mathematics and Mathematical Sciences |
| title | On hypersurface quotient singularities of dimension 4 |
| title_full | On hypersurface quotient singularities of dimension 4 |
| title_fullStr | On hypersurface quotient singularities of dimension 4 |
| title_full_unstemmed | On hypersurface quotient singularities of dimension 4 |
| title_short | On hypersurface quotient singularities of dimension 4 |
| title_sort | on hypersurface quotient singularities of dimension 4 |
| url | http://dx.doi.org/10.1155/S0161171204302140 |
| work_keys_str_mv | AT lichiang onhypersurfacequotientsingularitiesofdimension4 AT shishyrroan onhypersurfacequotientsingularitiesofdimension4 |