Defining equations of certain rational cuspidal curves. I
The curves which are studied in this paper are irreducible plane curves \(C\) (over the complex field) which possess only one singular point \(P\) which is a cusp (unicuspidal curve), and such that the line \(l\) which is the multiple tangent at \(P\) meets \(C\) only in \(P\) (curve of Abhyankar-Moh-Suzuki type, AMS type). The main result in the paper is a theorem which explains how to pass with Cremona transformation from a curve \(C\) of AMS type to a line through \(P\), gives the multiplicity sequence at \(P\) of every curve at each step and how the equations of the curves are related to each other. The main tools for the proof are a detailed study of the effect of elementary transformations on germs of curve and De Jonquières transformations.
scientific article; zbMATH DE number 1546893