2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70117For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, called the Cox ring. We show that in characteristic 0 this ring is Gorenstein and its spectrum has rational singularities. Also a gap in math.AG/0309111 is pointed out.12 pages, LateX, uses XY-PicAlgebraic Geometry14J26; 14J17text