Threefolds with one apparent double point

Abstract

The number of apparent double points of an irreducible projective variety X of dimension n in $$\mathbb {P}^{2n+1}$$ is the number of secant lines to X passing through a general point of $$\mathbb {P}^{2n+1}$$ . This classical notion dates back to Severi. Smooth threefolds having one apparent double point have been classified in 2004 by Ciliberto, Mella and Russo. This paper presents examples and a partial classification of singular threefolds having one apparent double point.