Relative blocking sets of unions of Baer subplanes

摘要

We show that, for small t, the smallest set that blocks the long secants of the union of t pairwise disjoint Baer subplanes in PG(2,q2) has size t(q+1) and consists of t Baer sublines, and, for large t, the smallest such set has size q2+q+1 and is itself a Baer subplane of PG(2,q2). We also present a stability result in the first case.