IJPAM: Volume 35, No. 2 (2007)

BASE LOCI OF HOMOGENEOUS FORMS IN
THE PROJECTIVE PLANE OVER A FINITE FIELD

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix a finite set $S \subset {\bf {P}}^2$ defined over $\mathbb {F}_q$. Here we give conditions on $e\ge 1$, $d$ and $S$ such that there is a degree $d$ plane curve defined over $\mathbb {F}_{q^e}$, containing $S$ and avoiding another fixed finite subset of ${\bf {P}}^2$.

Received: December 11, 2006

AMS Subject Classification: 14N05

Key Words and Phrases: finite projective plane, homogeneous form, base locus

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2