2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217948The Picard scheme of a smooth curve and a smooth complex variety is reduced. In this note we discuss which classes of surfaces in terms of the Enriques-Kodaira classification can have non-reduced Picard schemes and whether there are restrictions on the characteristic of the ground field. It turns out that non-reduced Picard schemes are uncommon in Kodaira dimension $κ\leq0$, that this phenomenon can be bounded for $κ=2$ (general type) and that it is as bad as can be in $κ=1$.7 pages, simplified and improved versionAlgebraic Geometry14K30; 14J10text