On the Nagata conjecture
| dc.creator | Roé, Joaquim | |
| dc.date | 2003-04-09 | |
| dc.date.accessioned | 2026-07-07T04:56:44Z | |
| dc.date.available | 2026-07-07T04:56:44Z | |
| dc.description | T. Szemberg proposed in 2001 a generalization to arbitrary varieties of M. Nagata's 1959 open conjecture, which claims that the Seshadri constant of r>9 very general points of the projective plane is maximal. Here we prove that Nagata's original conjecture implies Szemberg's for all smooth surfaces X with an ample divisor L generating its Neron-Severi group and such that L^2 is a square. More generally, we prove that the (n-1)-dimensional Seshadri constant of an ample divisor L on a projective variety X of dimension n at r very general points is bounded below by the product of the (n-1)-dimensional Seshadri constant of at a very general point times the (n-1)-dimensional Seshadri constant of the hyperplane on projective n-space at r very general points. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304124 | |
| dc.identifier | http://arxiv.org/abs/math/0304124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67031 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14C20 | |
| dc.title | On the Nagata conjecture | |
| dc.type | text |