English

The plane Jacobian conjecture for rational curves

Algebraic Geometry 2019-07-09 v3

Abstract

Let K be an algebraically closed field of characteristic zero and let f(x,y) be a nonzero polynomial of K[x,y]. We prove that if the generic element of the family (fλ)_λ(f-\lambda)\_{\lambda} is a rational polynomial, and if the Jacobian J(f,g) is a nonzero constant for some polynomial g in K[x,y], then K[f,g] =K[x,y].

Keywords

Cite

@article{arxiv.1807.03991,
  title  = {The plane Jacobian conjecture for rational curves},
  author = {Abdallah Assi},
  journal= {arXiv preprint arXiv:1807.03991},
  year   = {2019}
}

Comments

The paper has been withdrawn due to an incomplete argument in the main result (page 4)

R2 v1 2026-06-23T02:57:23.705Z