2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58974Let X be a projective variety which is covered by a family of rational curves of minimal degree. The classic bend-and-break argument of Mori asserts that if x and y are two general points, then there are at most finitely many curves in that family which contain both x and y. In this work we shed some light on the question as to whether two sufficiently general points actually define a unique curve. As an immediate corollary to the results of this paper, we give a characterization of projective spaces which improves on the known generalizations of Kobayashi-Ochiai's theorem.Reason for resubmission: improved expositionAlgebraic Geometry14J45; 14C15text