IJPAM: Volume 56, No. 2 (2009)

CURVES OVER $\mathbb {F}_q$ THROUGH
POINTS IN A HYPERBOLIC QUADRIC SURFACE
AND IN HIRZEBRUCH SURFACES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X$ be either a hyperbolic quadric surface over $\mathbb {F}_q$ or a Hirzebruch surface. Here we give conditions for the existence of a curve $C \subset X$ defined over $\mathbb {F}_q$ and containing $X(\mathbb {F}_q)$ or a prescribed subset of it.

Received: August 13, 2009

AMS Subject Classification: 14N05, 12E20

Key Words and Phrases: hyperbolic quadric surface, Hirzebruch surface, curves over a finite field

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 2