Mohammed Abuelhassan

On the Classification of Rational Plane Curves of Type (D,m): Rational Plane Curves of Types (D,d-2) and (D,d-3,1) Mohammed Abuelhassan

Let C?P²=P²(C) be a rational plane curve of degree d and let ? denote the maximal multiplicity of the singular points of C. We say that C is of type (d,?). Let P?C be a singular point, and let r_{P} be the number of the branches of C at P. Set ?(C)=?_{P?Sing(C)}(r_{P}-1). We say that C is of type (d,?,?) if C is of type (d,?) and ?=?(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).