2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62844We study smooth threefolds of the projective space of dimension 5 whose quadrisecant lines don't fill up the space. We give a complete classification of those threefolds X whose only quadrisecant lines are the lines contained in X. Then we prove that, if X admits "true" quadrisecant lines, but they don't fill up the space, then either X is contained in a cubic hypersurface, or it contains a family of dimension at least two of plane curves of degree at least four.Plain Tex, 12 pagesAlgebraic Geometry14J30, 14J70text