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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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Preprints, Working Papers, ...
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Contributor : Abdallah Assi Connect in order to contact the contributor
Submitted on : Monday, October 21, 2013 - 3:31:17 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:52 AM
Long-term archiving on: : Friday, April 7, 2017 - 2:14:06 PM


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  • HAL Id : hal-00712409, version 2
  • ARXIV : 1206.6189



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



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