Sagbi Bases of Cox-Nagata Rings
| dc.creator | Sturmfels, Bernd | |
| dc.creator | Xu, Zhiqiang | |
| dc.date | 2008-03-06 | |
| dc.date | 2008-03-11 | |
| dc.date.accessioned | 2026-07-07T09:25:47Z | |
| dc.date.available | 2026-07-07T09:25:47Z | |
| dc.description | We degenerate Cox-Nagata rings to toric algebras by means of sagbi bases induced by configurations over the rational function field. For del Pezzo surfaces, this degeneration implies the Batyrev-Popov conjecture that these rings are presented by ideals of quadrics. For the blow-up of projective n-space at n+3 points, sagbi bases of Cox-Nagata rings establish a link between the Verlinde formula and phylogenetic algebraic geometry, and we use this to answer questions due to D'Cruz-Iarobbino and Buczynska-Wisniewski. Inspired by the zonotopal algebras of Holtz and Ron, our study emphasizes explicit computations, and offers a new approach to Hilbert functions of fat points. | |
| dc.description | 35 pages. Results in Section 7 improved | |
| dc.identifier | https://arxiv.org/abs/0803.0892 | |
| dc.identifier | http://arxiv.org/abs/0803.0892 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156524 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 14Q99; 05A15 | |
| dc.title | Sagbi Bases of Cox-Nagata Rings | |
| dc.type | text |