On the Classification of Rational Plane Curves of Type (d,m)

Let C⊂P²=P²(C) be a rational plane curve of degree d and let ν denote the maximal multiplicity of the singular points of C. We say that C is of type (d,ν). Let P∈C be a singular point, and let r_{P} be the number of the branches of C at P. Set ι(C)=∑_{P∈Sing(C)}(r_{P}-1). We say that C is of type (d,ν,ι) if C is of type (d,ν) and ι=ι(C). We classify all rational plane curves of type (d,d-2). We give the complete list of all rational plane curves of type (d,d-2). In particular, we provide an inductive algorithm to construct such curves. Furthermore, we show that any such curve C is transformable into a line by a Cremona transformation. We also construct some classes of rational plane curves of type (d,d-3,1).