2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63941We study the ring of sections A(X) of a complete symmetric variety X, that is of the wonderful completion of G/H where G is an adjoint semi-simple group and H is the fixed subgroup for an involutorial automorphism of G. We find generators for Pic(X), we generalize the PRV conjecture to complete symmetric varieties and construct a standard monomial theory for A(X) that is compatible with G orbit closures in X. This gives a degeneration result and the rational singularityness for A(X).15 pages, LatexAlgebraic GeometryRepresentation Theory14M17 (Primary) 14L30 (Secondary)text