On 1-Blocking Sets in PG(n,q), n≥3

Abstract

In this article we study minimal 1-blocking sets in finite projective spaces PG(n,q), n \geq 3. We prove that in PG(n,q^2), q =p^h , p prime, p >3 , h\geq1, the second smallest minimal 1-blocking sets are the second smallest minimal blocking sets, w.r.t. lines, in a plane of PG(n,q^2). We also study minimal 1-blocking sets in PG(n,q^3), n \geq 3, q=p^h, p prime, p >3 , q \neq 5, and prove that the minimal 1-blocking sets of cardinality at most q^3+q^2+q+1 are either a minimal blocking set in a plane or a subgeometry PG(3,q).