IJPAM: Volume 18, No. 2 (2005)

LINEAR SYSTEMS ON THE FINITE PROJECTIVE
PLANE: INTERPOLATION AND BASE POINTS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Here we want to discuss a few interpolation problems for linear systems on a projective space over a finite field. For instance, we prove the following result. Fix an integer $d \ge 3$, a field $K$ containing at least $d+1$ points and $P\in {\bf {P}}^2_K$. Set $m_1:= d-2$, $m_j:= 2$ for $2 \le j \le d-1$ and $m_i:= 1$ for $d \le i \le d+2$. Then there are points $P_i\in {\bf {P}}^2_K$, $1 \le i \le d+2$ such that $h^0({\bf {P}}^2_K, \mathcal {I}_{m_1P_1\cup \cdots \cup m_{d+2}P_{d+2}}(d)) = 2$ and the linear system $H^0({\bf {P}}^2_K, \mathcal {I}_{m_1P_1\cup \cdots \cup m_{d+2}}(d))$ has $P$ as the only base point outside $\{P_1,\dots ,P_{d+2}\}$.

Received: July 11, 2004

AMS Subject Classification: 14N05, 11T99

Key Words and Phrases: finite projective space, base points of linear systems, interpolation over a finite field

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 2