Geodesic
A note on the plane Jacobian conjecture
Nguyen Van Chau1
1Institute of Mathematics Vietnam Academy of Science and Technology 18 Hoang Quoc Viet 10307 Hanoi,Vietnam
Annales Polonici Mathematici, Volume 105 (2012) no. 1, pp. 13-19

See the original article notice from the Institute of Mathematics Polish Academy of Sciences source

It is shown that every polynomial function $P:\mathbb{C}^2\to\mathbb{C}$ with irreducible fibres of the same genus must be a coordinate. Consequently, there do not exist counterexamples $F=(P,Q)$ to the Jacobian conjecture such that all fibres of $P$ are irreducible curves with the same genus.
DOI: 10.4064/ap105-1-2
Keywords: shown every polynomial function mathbb mathbb irreducible fibres genus coordinate consequently there exist counterexamples jacobian conjecture fibres irreducible curves genus

Nguyen Van Chau  1

1 Institute of Mathematics Vietnam Academy of Science and Technology 18 Hoang Quoc Viet 10307 Hanoi,Vietnam 
Nguyen Van Chau. A note on the plane Jacobian conjecture. Annales Polonici Mathematici, Volume 105 (2012) no. 1, pp. 13-19. doi: 10.4064/ap105-1-2
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