Boundedness for codimension two submanifolds of quadrics

Arrondo, 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).