On the Number of Cusps of Rational Cuspidal Plane Curves

Abstract

A cuspidal curve is a curve whose singularities are all cusps, i.e., unibranched singularities. This article describes computations that lead to the following conjecture: A rational cuspidal plane curve of degree greater than or equal to six has at most three cusps. The curves with precisely three cusps occur in three series. Assuming the Flenner--Zaidenberg rigidity conjecture, the above conjecture is verified up to degree $20$