Blocking Sets of Type (1, k) in a Finite Projective Plane

Following a previous work of Tallini (J. Geom. (1987), 191–199), we investigate the arithmetical properties of a blocking set in a finite projective plane which is met by any line in either 1 or k points, for a fixed number k. The results are then used to give some characterizations of blocking sets of this type which are preserved by a large collineation group of the plane.