2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110061Let S_r be the blow-up of P^2 in r general points, i.e., a smooth Del Pezzo surface of degree 9-r. For r <= 7, we determine the quadratic equations defining its Cox ring explicitly. The ideal of the relations in Cox(S_8) is calculated up to radical. As conjectured by Batyrev and Popov, all the generating relations are quadratic.17 pagesAlgebraic Geometry14J26 (Primary) 14C20 (Secondary)text