Nontrivial rational polynomials in two variables have reducible fibres

Details Nontrivial rational polynomials in two variables have reducible fibres Nontrivial rational polynomials in two variables have reducible fibres

1998-05-21

arxiv.org/abs/math/9805093v1

Bull. Austral. Math. Soc. 58 (1998), no. 3, 501--503

Mathematics

Algebraic Geometry

1 1/2 pages

Scientific paper

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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