Finite Laguerre Near-planes of Odd Order Admitting Desarguesian Derivations

AbstractWe introduce finite Laguerre near-planes and investigate such planes of odd order that admit a Desarguesian derivation

Blocking sets of the Hermitian unital

It is known that the classical unital arising from the Hermitian curve in PG(2,9) does not have a 2-coloring without monochromatic lines. Here we show that for q≥4 the Hermitian curve in PG(2,q2) does possess 2-colorings without monochromatic lines. We present general constructions and also prove a lower bound on the size of blocking sets in the classical unital