Quotients of Calabi-Yau varieties
| dc.creator | Kollár, János | |
| dc.creator | Larsen, Michael | |
| dc.date | 2007-01-17 | |
| dc.date | 2007-01-21 | |
| dc.date.accessioned | 2026-07-07T07:41:50Z | |
| dc.date.available | 2026-07-07T07:41:50Z | |
| dc.description | Let $X$ be a complex Calabi-Yau variety, that is, a complex projective variety with canonical singularities whose canonical class is numerically trivial. Let $G$ be a finite group acting on $X$ and consider the quotient variety $X/G$. The aim of this paper is to determine the place of $X/G$ in the birational classification of varieties. That is, we determine the Kodaira dimension of $X/G$ and decide when it is uniruled or rationally connected. If $G$ acts without fixed points, then $κ(X/G)=κ(X)=0$; thus the interesting case is when $G$ has fixed points. We answer the above questions in terms of the action of the stabilizer subgroups near the fixed points. We give a rough classification of possible stabilizer groups which cause $X/G$ to have Kodaira dimension $-\infty$ or equivalently (as we show) to be uniruled. These stabilizers are closely related to unitary reflection groups. | |
| dc.description | Theorem 3 has been corrected. 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701466 | |
| dc.identifier | http://arxiv.org/abs/math/0701466 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122260 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 14J32, 14K05, 20E99 (Primary) 14M20, 14E05, 20F55 (Secondary) | |
| dc.title | Quotients of Calabi-Yau varieties | |
| dc.type | text |