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.