Small Blocking Sets in Higher Dimensions

Small Blocking Sets in Higher Dimensions

We show that small blocking sets in PG(n, q) with respect to hyperplanes intersect every hyperplane in 1 modulo p points, where q= p. The result is then extended to blocking sets with respect to k-dimensional subspaces and, at least when p>2, to intersections with arbitrary subspaces not just hyperplanes. This can also be used to characterize certain non-degenerate blocking sets in higher dimen...

Symmetries of Julia sets in higher dimensions

On small blocking sets and their linearity

We prove that a small blocking set of PG(2, q) is “very close” to be a linear blocking set over some subfield GF(p) < GF(q). This implies that (i) a similar result holds in PG(n, q) for small blocking sets with respect to k-dimensional subspaces (0 ≤ k ≤ n) and (ii) most of the intervals in the interval-theorems of Szőnyi and Szőnyi-Weiner are empty.

Characterization results on small blocking sets

In [8], De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q+(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 3, of size at most 3n + 3n−2. This means that the three smallest minim...

On the stability of small blocking sets

A stability theorem says that a nearly extremal object can be obtained from an extremal one by “small changes”. In this paper, we study the relation of sets having few 0-secants and blocking sets.