Algorithms for curves with one place at infinity

Abstract

Let f be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated δ-sequence, and consequently its value semigroup. For a δ-sequence we present a procedure to construct all curves having this associated sequence. Also for a fixed genus (equivalently Frobenius number) we construct all δ-sequences generating numerical semigroups with this given genus.We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.