On Hypersurface Quotient Singularity of Dimension 4
| dc.creator | Chiang, Li | |
| dc.creator | Roan, Shi-Shyr | |
| dc.date | 2000-11-21 | |
| dc.date | 2004-10-26 | |
| dc.date.accessioned | 2026-07-07T04:38:42Z | |
| dc.date.available | 2026-07-07T04:38:42Z | |
| dc.description | We consider geometrical problems on Gorenstein hypersurface orbifolds of dimension $n \geq 4$ through the theory of Hilbert scheme of group orbits. For a linear special group $G$ acting on $\CZ^n$, we study the $G$-Hilbert scheme, $\hl^G(\CZ^n)$, and crepant resolutions of $\CZ^n/G$ for $G$=the $A$-type abelian group $ A_r(n)$. For $n=4$, we obtain the explicit structure of $\hl^{A_r(4)}(\CZ^4)$. The crepant resolutions of $\CZ^4/A_r(4)$ are constructed through their relation with $\hl^{A_r(4)}(\CZ^4)$, and the connections between these crepant resolutions are found by the "flop" procedure of 4-folds. We also make some primitive discussion on $\hl^G(\CZ^n)$ for the $G$= alternating group ${\goth A}_{n+1}$ of degree $n+1$ with the standard representation on $\CZ^n$; the detailed structure of $\hl^{{\goth A}_4}(\CZ^3)$ is explicitly constructed. | |
| dc.description | 27 pages, Latex, 11 figures, Some reorganizations and improvement of presentations, Typos corrected, Arguments of Theorem 1 of section 3 in the earlier version are refined with clearer explanation for the justification of contradicting statement appeared in a published journal literature by some other author | |
| dc.identifier | https://arxiv.org/abs/math/0011151 | |
| dc.identifier | http://arxiv.org/abs/math/0011151 | |
| dc.identifier | IJMMS 2004:48 (2004) 2547-2581 | |
| dc.identifier | doi:10.1155/S0161171204302140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60388 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J35, 14J30, 14M25, 20C30 | |
| dc.title | On Hypersurface Quotient Singularity of Dimension 4 | |
| dc.type | text |