Rational curves with one place at infinity

Abdallah Assi (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

Let K be an algebraically closed field of characteristic zero. Given a polynomial f(x,y) in K[x,y] with one place at infinity, we prove that either f is equivalent to a coordinate, or the family (f+c) has at most two rational elements. When (f+c) has two rational elements, we give a description of the singularities of these elements.

Mots clés: Rational curves Curves with one place at infinity

Domaines: Géométrie algébrique [math.AG]

Abdallah Assi. Rational curves with one place at infinity. 2012. ⟨hal-00712409v2⟩