2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62772We study families of linear spaces in projective space whose union is a proper subvariety X of the expected dimension. We establish relations between configurations of focal points and existence or non-existence of a fixed tangent space to X along a general element of the family. We apply our results to the classification of ruled 3-dimensional varieties.To be published in Illinois Journal of MathematicsAlgebraic Geometry14N20, 14J30text