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Rational curves with one place at infinity

Abstract

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.
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Dates and versions

hal-00712409 , version 1 (27-06-2012)
hal-00712409 , version 2 (21-10-2013)

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