Let Γ be a differentiable curve
in a real projective plane P2 intersected by every line at a finite number of points. A
point of Γ is ordinary if Γ is locally convex at that point; otherwise, the point is
singular. Let the singular points of Γ consist of n1 inflections, n2 cusps (cusps of the
first kind) and n3 beaks (cusps of the second kind). Then Γ is singular if
n(Γ) = n1+ n2+ n3> 0; otherwise, Γ is non-singular. The following questions arise
naturally: Under what conditions is Γ singular? What is then the minimum value of
n(Γ) and is it dependent or independent of the type of singularities that Γ may
possess? Presently, we determine a class of curves Γ for which n(Γ) ≥ 2 but
n1+ 2n2+ n3≥ 4.
