Some remarks on factoriality of certain hypersurfaces in $\mathbb{P}^4 $

Abstract

Let V be a reduced and irreducible hypersurface of degree k ≧ 3. In this paper we prove that if the singular locus of V consists of δ2 ordinary double points, δ3 ordinary triple points and if δ2 + 4δ3 < (k − 1)2, then any smooth surface contained in V is a complete intersection on V.