Factoriality of Certain Threefolds Complete Intersection in P⁵ with Ordinary Double Points

Abstract

Let V ⊂ P ⁵ be a reduced and irreducible threefold of degree s, complete intersection on a smooth hypersurface of degree t, with s > t ² − t. In this paper, we prove that if the singular locus of V consists of δ < 3s/8t ordinary double points, then any projective surface contained in V is a complete intersection on V. In particular, V is Q-factorial.

Key Words:

• Projective complete intersection
• Ordinary double point
• Factoriality
• Castelnuovo–Halphen theory
• Hodge theory
• Lefschetz theorems

Mathematics Subject Classification:

• Primary 14C22
• Secondary 14J17, 14M10, 14M05, 14H99

Acknowledgments

Notes

^#Communicated by L. Ein.