Semi-group conditions for affine algebraic plane curves with more than on place at infinity (Q2472513)

A result of [\textit{S. S. Abhyankar} and \textit{Moh} [in: Lectures on expansion techniques in algebraic geometry. With notes by Balwant Singh. Lect. Math. Phys. Tata Institute of Fundamental Research. 57 (1977; Zbl 0818.14001)] completely describes the possible links at infinity for plane algebraic curves with one place at infinity. In this paper the author generalizes such a description in two cases: the case of one point at infinity and the case of more points at infinity. She makes use of splice diagrams (i.e. trees with integer weight at the ends of edges), first described by \textit{W. D. Neumann} [Invent. Math. 98, No. 3, 445--489 (1989; Zbl 0734.57011)]. A new elementary proof of Abhyankar-Moh result is also provided; this relies on a study of the Newton polygons that are used in finding the Newton-Puiseux expansion of the polynomial defining the curve.