2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60071Given a flat, projective morphism $Y \to T$ from an equidimensional scheme to a nonsingular curve and a subscheme $Z$ of $Y$, we give conditions under which specialization of the Segre class $s(N_{Z}Y)$ of the normal cone of $Z$ in $Y$ implies flatness of the normal cone. We apply this result to study when the relative tangent star cone of a flat family is flat.LaTeX, 11 pages, no figuresAlgebraic GeometryCommutative Algebra13A30 14C17 (Primary) 14B25 14M05 (Secondary)text