2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77723We give a criterion for a continuous family of curves on a nodal $K$-trivial threefold $X_0$ to contribute geometrically rigid curves to a general smoothing of $X_0$. As an application, we prove the existence of geometrically rigid curves of arbitrary degree and explicitly bounded genus on general complete intersection Calabi-Yau threefolds.8 pages, LaTeX2eAlgebraic Geometry14C05, 14J32 (Primary); 14C25, 14J28 (Secondarytext