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