IJPAM: Volume 65, No. 1 (2010)

$3$-FOLDS $X \subset \mathbb {P}^7$ WITH
A HYPERSURFACE OF POINTS WITH $X$-RANK $\ge 3$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X\subset \mathbb {P}^{2m+1}$, $m \in \{2,3\}$, be a smooth and non-defective subvariety. Here we prove that there is a hypersurface of $\mathbb {P}^{2m+1}$ formed by points with $X$-rank $\ge 3$ if and only if $X$ is an OADP (a variety with one apparent double point). All such surfaces and three-folds are classified by Ciliberto, Mella and Russo.

Received: June 23, 2010

AMS Subject Classification: 14N05, 14J99

Key Words and Phrases: ranks, tangent developable, variety with OADP

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 1