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

Abstract

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.