Factoriality of certain hypersurfaces of ${bold P^4}$ with ordinary double points.

Let $V\subset \bold P^4$ be a reduced and irreducible hypersurface of degree $k\geq 3$, whose singular locus consists of $\delta$ ordinary double points. In this paper we prove that if $\delta < k/2$, or the nodes of $V$ are set-theoretic intersection of hypersurfaces of degree $n<k/2$ and $\delta < (k-2n)(k-1)^2/k$, then any projective surface contained in $V$ is a complete intersection on $V$. In particular $V$ is ${\bold Q}$-factorial. We give more precise results for {\it {smooth}} surfaces contained in $V$.