IJPAM: Volume 36, No. 2 (2007)

SUBSPACES OF A FINITE PROJECTIVE SPACE
CONTAINING MANY POINTS OF A GIVEN SET

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


Abstract.Fix $S \subseteq {\bf {P}}^n(\mathbb {F}_q)$. For each integer $1 \le t < n$ let $\sigma (S,t)$ denote the maximal number of points of $S$ contained in a $t$-dimensional linear subspace. Here we compute these integers (for certain $t$) when $S$ arises from Veronese varieties or embeddings of a hyperbolic or an elliptic quadric surface.

Received: February 11, 2007

AMS Subject Classification: 14N05, 05C38

Key Words and Phrases: elliptic quadric surface, Veronese variety, finite projective space, hyperbolic quadric surface

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 2