Classical Varieties and Caps

Abstract

Let $PG(n,q)$ be the projective $n$-space over the Galois field $GF(q)$. A $k$-cap in $PG(n,q)$ is a set of $k$ points such that no three of them are collinear. A $k$-cap is said to be complete if it is maximal with respect to set-theoretic inclusion. In this paper, using classical algebraic varieties, such as Segre varieties and Veronese varieties, some new infinite classes of caps are constructed.