Nontrivial rational polynomials in two variables have reducible fibres

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dc.creatorNeumann, Walter D.
dc.creatorNorbury, Paul
dc.date1998-05-21
dc.date.accessioned2026-07-07T05:24:48Z
dc.date.available2026-07-07T05:24:48Z
dc.descriptionIt 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 $C^2$.
dc.description1 1/2 pages
dc.identifierhttps://arxiv.org/abs/math/9805093
dc.identifierhttp://arxiv.org/abs/math/9805093
dc.identifierBull. Austral. Math. Soc. 58 (1998), no. 3, 501--503
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76947
dc.subjectAlgebraic Geometry
dc.titleNontrivial rational polynomials in two variables have reducible fibres
dc.typetext

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