On Arcs and Curves with Many Automorphisms

We construct highly symmetric arcs by using highly symmetric curves: the Klein quartic which is the most symmetric non-singular curve of degree 4, and the Wiman sextic which is shown to be the unique A₆-invariant curve of degree 6. The set of flexes of the Klein quartic is a 24-arc with automorphism group PSL(2, 7), while the set of flexes of the Wiman sextic is a 72-arc with automorphism group PSL(2, 9) A₆.This research was carried out with the support of the Italian MIUR (Progetto Strutture geometriche, combinatoria e loro applicazioni) and of GNSAGA.