Conics and multiple derivation

Let C ¯ be a conic in PG ( 2 , q 2 ) and suppose we derive with respect to a derivation set or multiple derivation set. This paper looks at whether the conic C ¯ gives rise to an inherited arc in the derived plane. Further, we construct two families of conics which give rise to inherited arcs after certain double derivations. Finally we construct a family of complete ( q 2 + 1 ) -arcs in certain André planes.