Semi-group Conditions for Affine Algebraic Plane Curves with More than One Place at Infinity

An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh [1] completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity