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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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https://hal.archives-ouvertes.fr/hal-00712409
Contributor : Abdallah Assi <>
Submitted on : Monday, October 21, 2013 - 3:31:17 PM
Last modification on : Monday, March 9, 2020 - 6:16:03 PM
Document(s) archivé(s) le : Friday, April 7, 2017 - 2:14:06 PM

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

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

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