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The plane Jacobian conjecture for rational curves
Published 11 Jul 2018 in math.AG | (1807.03991v3)
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 $(f-\lambda)_{\lambda}$ 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].
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