The Return of the Baer Subplane

We discuss the notion of a tangency set in a projective plane, generalising the well-studied idea of a minimal blocking set. Tangency sets have recently been used in connection with the coding theory related to algebraic curves over finite fields, and they are closely related to the strong representative systems introduced by T. Illés, T. Szonyi, and F. Wettl (1991,Mitt. Math. Sem. Giessen201, 97–107). Here we give bounds on the possible sizes of tangency sets, and structural results are obtained in the extremal cases.