IJPAM: Volume 69, No. 1 (2011)

LINEAR PROJECTIONS OF
SMOOTH CURVES OVER A FINITE FIELD

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


Abstract. Let $C\subset \mathbb {P}^n$ be a smooth curve defined over $\mathbb {F}_q$ with degree $d$ and genus $g$. Here we give conditions on $d, g, q$ which assures the existence of an isomorphic linear projection into $\mathbb {P}^3$ (case $n\ge 4$) or a birational projection into $\mathbb {P}^2$ with only double points and defined over $\mathbb {F}_q$.

Received: December 18, 2010

AMS Subject Classification: 14H50, 14N05, 14Q05, 11T99

Key Words and Phrases: linear projection, smooth space curve, finite field

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1