IJPAM: Volume 60, No. 1 (2010)

CUSPIDAL PROJECTIONS OF SPACE CURVES

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


Abstract.Let $X \subset \mathbb {P}^3$ be an integral and non-degenerate curve. A point $O\in \mathbb {P}^3\backslash X$ is said to give a cuspidal projection of $X$ if the linear projection from $O$ induces an injective map $X \to \mathbb {P}^2$. Here we produce two classes of pairs $(X,O)$ with $O$ inducing a cuspidal projection of $X$. In the second class (only in positive characteristic) $X$ is contained in a smooth quadric surface $\Sigma$ and we may take as $O$ any point of $\Sigma\backslash X$.

Received: January 14, 2010

AMS Subject Classification: 14H50

Key Words and Phrases: space curve, cuspidal projection, $X$-rank

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 1