2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150321Arrondo, Sols and De Cataldo proved that there are only finitely many families of codimension two subvarieties not of general type in the smooth quadric of dimension $n+2$ for $n\ge 2 $, $n\neq 4$. In this paper we drop the assumption $n\neq 4$ from the previous result (obviously the assumption $n\ge 2$ cannot be removed).AMS-LaTeX v2e, 22 pages, to the memory of Fernando SerranoAlgebraic Geometry14M07 (Primary) 14J70 (Secondary)text