IJPAM: Volume 78, No. 3 (2012)

CUSPIDAL PROJECTIONS OF
SMOOTH SPACE CURVES, II

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


Abstract. Let $C \subseteq \mathbb {P}^3$ be smooth curve and $P\in \mathbb {P}^3\setminus C$. We say that the linear projection $\ell _P$ of $C$ from $P$ is cuspidal if $\sharp (C\cap D)\le 1$ for every line $D\subset \mathbb {P}^3$ through $P$, i.e. if $\ell _P\vert C$ is birational onto its image and $\ell _P(C)$ has only unibranch singularities. Here we construct two large classes of curves (lying in quadric surfaces) with at least one cuspidal projection. We also consider inner cuspidal projections (from points of $C$) and the $C$-rank of lines.

Received: March 22, 2012

AMS Subject Classification: 14N05

Key Words and Phrases: space curve, cuspidal projection, linear projection, inner projection

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 3