Constructions of unitals in Desarguesian planes

We present a new construction of non-classical unitals from a classical unital UU in PG(2,q2). The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model ΠΠ of PG(2,q2) with the following three properties: (i)points of ΠΠ are those of PG(2,q2);(ii)lines of ΠΠ are certain lines and conics of PG(2,q2);(iii)the points in UU form a non-classical B–M unital in ΠΠ. Our construction also works for the B–T unital, provided that conics are replaced by certain algebraic curves of higher degree.