Blocking sets of Hermitian generalized quadrangles

Generalized quadrangles, flocks, and BLT sets

Approximately five years ago Thas observed a remarkable coincidence relating certain generalized quadrangles constructed in [Ka3] to flocks of cones and translation planes [Th] (cf. [Ka2]). While there is a rapidly growing literature concerning this connection, there as yet has been no explanation for it. This note contains an observation providing at least some kind of explanation. It also con...

Ovoidal blocking sets and maximal partial ovoids of Hermitian varieties

In [1], minimal large blocking sets in PG(3, q) and PG(4, q) havebeen constructed starting from ovoids of PG(3, q), Q(4, q) and Q(6, q).Some of these can be embedded in a hermitian variety as maximalpartial ovoids. In this paper, the geometric conditions assuring theseembeddings are established.References[1] F. Mazzocca, L. Storme and O. Polverino: Blocking sets in<l...

Characterizations of Generalized Quadrangles by Generalized Homologies

Let S= (P, B, I) be a generalized quadrangle of order (s, t). For X, y E P, X+ y. let X(x, y) be the group of all collineations of S fixing x and y linewise. If ZE (4 YJL> then the set of all points incident with the line xz (resp. y;) is denoted by z(resp. 3. The generalized quadrangle S = (P, B, I) is said to be (x, y)-transitive, x+ y, if X(x, y) is transitive on each set Z{x, z} and jZ’-{ y...

Finite Generalized Quadrangles

Intriguing Sets of Partial Quadrangles

Finite geometry is the study of incidence structures, a system of points and lines with some points on some lines according to an incidence relation, such that the number of points and lines is finite. Generalised quadrangles arose from an effort by Tits [5] to give geometric constructions of the finite simple groups of Lie type. Tits' key observation was that the incidence graph of an n-gon al...