The Cox ring of a Del Pezzo surface
| dc.creator | Batyrev, Victor V. | |
| dc.creator | Popov, Oleg N. | |
| dc.date | 2003-09-05 | |
| dc.date.accessioned | 2026-07-07T05:00:54Z | |
| dc.date.available | 2026-07-07T05:00:54Z | |
| dc.description | Let $X_r$ be a smooth Del Pezzo surface obtained from $¶^2$ by blowing up $r \leq 8$ points in general position. It is well known that for $r \in \{3,4,5,6,7,8 \}$ the Picard group $\Pic(X_r)$ contains a canonical root system $R_r \in \{A_2 \times A_1, A_4, D_5, E_6, E_7, E_8 \}$. We prove some general properties of the Cox ring of $X_r$ ($r \geq 4$) and show its similarity to the homogeneous coordinate ring of the orbit of the highest weight vector in some irreducible representation of the algebraic group $G$ associated with the root system $R_r$. | |
| dc.description | AMS-LaTeX, 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0309111 | |
| dc.identifier | http://arxiv.org/abs/math/0309111 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68490 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Cox ring of a Del Pezzo surface | |
| dc.type | text |