Characterization results on small blocking sets of the polar spaces Q +(2n + 1, 2) and Q +(2n + 1, 3)

Abstract

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 3 n + 3 n−2 . This means that the three smallest minimal blocking sets of Q + (2n + 1, 3), n ≥ 3, are now classified. We present similar results for q = 2 by classifying the minimal blocking sets of Q + (2n + 1, 2), n ≥ 3, of size at most 2 n + 2 n−2 . This means that the two smallest minimal blocking sets of Q + (2n + 1, 2), n ≥ 3, are classified.