On the Classification of Rational Plane Curves of Type (d,m)
Rational Plane Curves of Types (d,d-2) and (d,d-3,1)
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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 ...
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).
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