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Nontrivial rational polynomials in two variables have reducible fibres

Walter D. Neumann·Paul Norbury
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Abstract

It has been proved several times in the literature that a polynomial map from $C^2$ to $C$ with irreducible rational fibers cannot be a component of a counterexample to the Jacobian Conjecture. This note points out that this result is empty: it is implicit in 1980 work of Miyanish and Sugie that such a polynomial is equivalent to $f(x,y)=x$ by a polynomial automorphism of $C^2$.

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Walter D. Neumann, Paul Norbury. 1998-05-21. Nontrivial rational polynomials in two variables have reducible fibres. https://arxiv.org/abs/math/9805093

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