A note on the plane Jacobian conjecture

@article{Chau2010ANO,
  title={A note on the plane Jacobian conjecture},
  author={Nguyen van Vinh Chau},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}
  • N. Chau
  • Published 21 May 2010
  • Mathematics
  • arXiv: Algebraic Geometry
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. 
1 Citations
Jacobian Pairs of Two Rational Polynomials are Automorphisms
It is shown that a polynomial map F = (P, Q) of ℂ2 is a polynomial automorphism of ℂ2 if J(P, Q) := PxQy − PyQx ≡ c ≠ 0 and, in addition, both of polynomials P and Q are rational, i.e., the generic

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