On curves with one place at infinity

Abdallah Assi (1) , Pedro A. García-Sánchez (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Departamento de Algebra

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 $\delta$-sequence, and consequently its value semigroup. Also for fixed genus (equivalently Frobenius number) we construct all $\delta$-sequences generating numerical semigroups with this given genus. For a $\delta$-sequence we present a procedure to construct all curves having this associated sequence. We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.

Mots clés: one place curve; semigroup of values; approximate roots

Domaines: Géométrie algébrique [math.AG]

Abdallah Assi, Pedro A. García-Sánchez. On curves with one place at infinity. 2014. ⟨hal-01016473⟩