2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104872We introduce a method to determine if n-dimensional smooth subvarieties of an ambient space of dimension at most 2n − 2 inherit the Picard group from the ambient space (as it happens when the ambient space is a projective space, according to results of Barth and Larsen). As an application, we give an affirmative answer (up to some mild natural numerical conditions) when the ambient space is a Grassmannian of lines (thus improving results of Barth, Van de Ven and Sommese) or a product of two projective spaces of the same dimension.20 pagesAlgebraic Geometry14C22text