2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150130A classification theorem is given of smooth threefolds of $\Bbb P^5$ covered by a family of dimension at least three of plane integral curves of degree $d\geq 2.$ It is shown that for such a threefold $X$ there are two possibilities: \item{(1)} $X$ is any threefold contained in a hyperquadric; \item{(2)} $d\leq 3$ and $X$ is either the Bordiga or the Palatini scroll.17 pages, to appear in Manuscripta Mathematica Plain TeXAlgebraic Geometry14J30 14M07text