Non-rational nodal quartic threefolds
| dc.creator | Cheltsov, Ivan | |
| dc.date | 2004-05-08 | |
| dc.date.accessioned | 2026-07-07T05:08:03Z | |
| dc.date.available | 2026-07-07T05:08:03Z | |
| dc.description | The $\mathbb{Q}$-factoriality of a nodal quartic 3-fold implies its non-rationality. We prove that a nodal quartic 3-fold with at most 8 nodes is $\mathbb{Q}$-factorial, and we show that a nodal quartic 3-fold with 9 nodes is not $\mathbb{Q}$-factorial if and only if it contains a plane. However, there are non-rational non-$\mathbb{Q}$-factorial nodal quartic 3-folds in $\mathbb{P}^4$. In particular, we prove the non-rationality of a general non-$\mathbb{Q}$-factorial nodal quartic 3-fold that contains either a plane or a smooth del Pezzo surface of degree 4. | |
| dc.identifier | https://arxiv.org/abs/math/0405150 | |
| dc.identifier | http://arxiv.org/abs/math/0405150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71107 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E08, 14J30, 14J45, 14J70, 14M20 | |
| dc.title | Non-rational nodal quartic threefolds | |
| dc.type | text |