The Cox ring of a Del Pezzo surface

Victor V. Batyrev, Oleg N. Popov

Let $X_r$ be a smooth Del Pezzo surface obtained from ${\P }^2$ by blowing up $r\le 8$ points in general position. It is well known that for $r\in \{3,4,5,6,7,8\}$ the Picard group…