On the equations for universal torsors over del Pezzo surfaces
| dc.creator | Serganova, Vera | |
| dc.creator | Skorobogatov, Alexei | |
| dc.date | 2008-06-01 | |
| dc.date.accessioned | 2026-07-07T09:42:05Z | |
| dc.date.available | 2026-07-07T09:42:05Z | |
| dc.description | We show that every split del Pezzo surface of degree d=5,4,3 or 2 has a universal torsor which is a dense open subset of the intersection of 6-d dilatations of the affine cone over the corresponding generalized Grassmannian G/P. Here a dilatation is the linear transformation by an element of the 'diagonal' torus. This gives a concise description of the quadratic equations of universal torsors obtained by Popov and Derenthal. Any (possibly, non-split) del Pezzo surface with a rational point has a universal torsor which embeds into the same homogeneous space as a split surface of the same degree. The proof uses a recent result of Ph. Gille and Raghunathan. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0806.0089 | |
| dc.identifier | http://arxiv.org/abs/0806.0089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162055 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | On the equations for universal torsors over del Pezzo surfaces | |
| dc.type | text |