A note on the plane Jacobian conjecture
classification
🧮 math.AG
math.AC
keywords
conjecturefibresgenusirreduciblejacobianmathbbsameconsequence
read the original abstract
It is shown that every polynomial function $P : \mathbb{C}^2\longrightarrow \mathbb{C}$ with irreducible fibres of same a genus is a coordinate. In consequence, there does not exist counterexamples F = (P,Q) to the Jacobian conjecture such that all fibres of P are irreducible curves of same a genus.
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