A note on the plane Jacobian conjecture

  title={A note on the plane Jacobian conjecture},
  author={Nguyen van Vinh Chau},
  journal={arXiv: Algebraic Geometry},
  • 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. 
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