2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117882We introduce the notion of monomial group action and study some of its consequences for Groebner basis theory. As an application we prove a conjecture of V. Batyrev and O. Popov describing the Cox rings of Del Pezzo surfaces (of degree at least 3) as quotients of a polynomial ring by an ideal generated by quadrics.29 pages, 3 figuresCommutative AlgebraAlgebraic Geometry13P10; 14J26text